helps you get there (when possible) Perpendicular Bisector SAS Alt. Int. Angles Theorem SAS AAS Reflexive **Property** Find the values **of** a and b that yields congruent **triangles** a = 6 b = 15 Quick Review! Given ABC is a **triangle**, find the measure **of** each angle. Then classify the **triangle** by its angles and sides. m A = 2x + 5°, m B = 3x – 15° and m C = 4x/

**Triangle** Proportionality Theorem. Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 2: Verifying Segments are Parallel Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles**/2 = 28= 30 + 5 = 35 Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Check It Out! Example 4 Find AC and DC. Substitute in given values./

planes intersect, then they intersect in exactly a line Undefined Terms **Properties** **of** Real Numbers ERHS Math Geometry Mr. Chin-Sung Lin Addition & Multiplication Operation **Properties** ERHS Math Geometry Mr. Chin-Sung Lin Closure Commutative **Property** Associative **Property** Identity **Property** Inverse **Property** Distributive **Property** Multiplication **Property** **of** Zero Closure ERHS Math Geometry Mr. Chin-Sung Lin Closure **property** **of** addition The sum **of** two real numbers is a real number a + b is/

**Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 2: Verifying Segments are Parallel Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of**/

: ASA, AAS, and HL Check It Out! Example 2 Given: Prove: NKL LMN. Holt McDougal Geometry 4-6 **Triangle** Congruence: ASA, AAS, and HL Statements Reasons 1. Given 2. Alternate Interior Angles Theorem 3. Reflexive **Property** **of** 4. ASA Postulate Holt McDougal Geometry 4-6 **Triangle** Congruence: ASA, AAS, and HL You can use the Third Angles Theorem to prove another congruence relationship based/

**properties**, or uses theorems to solve problems involving angles, lines, polygons, circles, or right **triangle** ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts GSE’s **Triangles** **Triangle**-figure formed by 3 segments joining 3 noncollinear pts. **Triangles** /24 + 4x+6 = 180 14x + 54 = 180 14x = 126 x = 9 Exterior Angles Thm The measure **of** an exterior angle **of** a **triangle** is equal to the sum **of** the measures **of** the 2 nonadjacent interior angles. m 1=m A+ m B m 1= + 1 A B/

, on pages #498-499 Note: To Take Classwork AND Homework from Lesson 7-1 (Classwork stapled on top) 04/02/14 Lesson #7-4, “Applying **Properties** **of** Similar **Triangles** " Objective: Use **properties** **of** similar **triangles** to find segment lengths. Apply proportionality and **triangle** angle bisector theorems. ACT: MEA-601 CC: G.18 CS: G-SRT2, G-SRT3, G-SRT5, T-29 Recourses: Holt-McDougal Geometry Textbook, Presentation/

BC 2. AD AD 2. Reflexive **property** 3.D is the midpoint **of** BC3. Definition **of** segment bisector ERHS Math Geometry A B C D Prove Congruent **Triangles** Mr. Chin-Sung Lin StatementsReasons 1.∆ ABC, AD is the bisector **of** BC, 1. Given and AD BC 2. AD AD 2. Reflexive **property** 3.D is the midpoint **of** BC3. Definition **of** segment bisector 4.BD DC 4. Definition/

Students will understand **properties** **of** circles. MM2G3 a Understand and use **properties** **of** chords, tangents, and secants as an application **of** **triangle** similarity. The measure **of** an arc formed by two adjacent arcs is the sum **of** the measures **of** the two arcs. Arc Addition Postulate MM2G3 Students will understand **properties** **of** circles. MM2G3 a Understand and use **properties** **of** chords, tangents, and secants as an application **of** **triangle** similarity. Find measures **of** arcs A recent/

x = 21y = 8 Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Use **properties** **of** similar **triangles** to find segment lengths. Apply proportionality and **triangle** angle bisector theorems. Objectives Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** (The pieces are proportional) (Top/Bottom=Top/Bottom) Holt McDougal Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 1: Finding the Length **of** a Segment Find US. Substitute 14 for RU, 4 for/

= 10.5 x = 21 Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** 7-4 Applying **Properties** **of** Similar **Triangles** Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Use **properties** **of** similar **triangles** to find segment lengths. Apply proportionality and **triangle** angle bisector theorems. Objectives Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Artists use mathematical techniques to make two/

**Properties** & Attributes A few polygons **Triangle** Quadrilateral (much more on these later) Pentagon Hexagon Heptagon Octagon Regular polygons are both equilateral and equiangular This would be called a regular pentagon because… Note that if you draw diagonals from any one vertex **of** a polygon to the remaining corners they divide the interior into **triangles** 4 sides gives you 2 **triangles** 5 sides gives you 3 **triangles**/

**Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 2: Verifying Segments are Parallel Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of**/

base angles are congruent. C-19 p. 205 **Triangle** **Properties** - Ch 4 Converse **of** the Isosceles **Triangle** Conjecture If a **triangle** has two congruent angles, then…. …it is an isosceles **triangle**. C-20 p. 206 **Triangle** **Properties** - Ch 4 **Triangle** Inequality Conjecture The sum **of** the lengths **of** any two sides **of** a **triangle** is …. ….greater than…. C-21 p. 214 …the length **of** the third side. **Triangle** **Properties** - Ch 4 Side-Angle Inequality Conjecture In/

14 MM2G3 Students will understand **properties** **of** circles. MM2G3 a Understand and use **properties** **of** chords, tangents, and secants as an application **of** **triangle** similarity. **Properties** **of** Tangents Essential Question: How do we use **properties** **of** a tangent to a circle? Thursday, January 21, 2016 Lesson 6.1 MM2G3 Students will understand **properties** **of** circles. MM2G3 a Understand and use **properties** **of** chords, tangents, and secants as an application **of** **triangle** similarity. Daily Homework Quiz 1/

. 1. 2. C A E A D B Reflexive **Property** Corresponding Angles Postulate Yes, by AA Similarity Not similar Scale factors must be equal! Lesson 4.3 Homework Lesson 4.3 – Similar **Triangles** –p7-8 Due Tomorrow Lesson 5.4 Using Similar **Triangles** Lesson 4.4 Objectives Identify corresponding parts **of** congruent figures. Solve similar **triangles**. (G2.3.4) Utilize the scale factor and proportions/

point **of** concurrency is the orthocenter **of** the **triangle**. The height **of** a **triangle** is the length **of** an altitude. Helpful Hint LT: I can apply **properties** **of** medians and altitudes **of** a **triangle** Holt Geometry Medians and Altitudes **of** **Triangles** Orthocenter ObtuseRightAcute LT: I can apply **properties** **of** medians and altitudes **of** a **triangle** Holt Geometry Medians and Altitudes **of** **Triangles** LT: I can apply **properties** **of** medians and altitudes **of** a **triangle** Holt Geometry Medians and Altitudes **of** **Triangles** Assignment/

congruent by SAS? In the figure below, point X is the midpoint **of**. Which statement, when added to the given information, is sufficient to prove that In each pair **of** **triangles**, parts are congruent as marked. Which pair **of** **triangles** is congruent by ASA? A B C D Supply the missing reasons below. a. ASA; CPCTC b. SSS; Reflexive **Property** c. SAS; Reflexive **Property** d. SAS; CPCTC

**Triangles** –A **triangle** is said to be inscribed in a circle if all **of** the vertices are points on the circle –Main **property**: if one **of** the sides is the diameter, the **triangle** IS a right **triangle**. Conversely, any inscribed right **triangle** has the diameter as one **of** its sides. –A right **triangle**/ at a point Quantitative Review Geometry – Lines and Angles –Exterior angles **of** a **triangle** a + b + c = 180; c + d = 180 d = a + b This **property** is frequently tested on GMAT –Parallel lines cut by a transversal: Sometimes/

corollary is a theorem that can be proved easily using another theorem. LT: I can use and apply **properties** **of** isosceles and equilateral **triangles**. Example 3A: Using **Properties** **of** Equilateral **Triangles** Find the value **of** x. ∆LKM is equilateral. (2x + 32) = 60 The measure **of** each **of** an equiangular ∆ is 60°. 2x = 28 Subtract 32 both sides. x = 14 Divide both sides by 2. Equilateral ∆ equiangular ∆ LT: I can/

angle 2. Given bisector 3. 1 2 3. Definition **of** angle bisector 4. 3 = 90 o, 4 = 90 o 4. Definition **of** perpendicular 5. 3 4 5. Substitution postulate 6. BD BD 6. Reflexive **property** A B C D 12 34 Scalene **Triangle** ERHS Math Geometry Mr. Chin-Sung Lin StatementsReasons 1. BD /1 2 1. Given 5 6 2. A B AB 2. Reflexive **Property** 3. ∆ ACB = ∆ ADB 3. ASA Postulate 4. A C AD 4. CPCTC 5. ∆ ADC is an isosceles **triangle** 5. Def. **of** Isosceles **Triangle** 6. 3 4 6. Base Angle Theorem A C B D O 1 2 5 /

, SAS You learned in Chapter 2 that the Reflexive, Symmetric, and Transitive **Properties** **of** Equality have corresponding **properties** **of** congruence. These **properties** also hold true for similarity **of** **triangles**. Holt McDougal Geometry 7-3 **Triangle** Similarity: AA, SSS, SAS Lesson Quiz 1. Explain why the **triangles** are similar and write a similarity statement. 2. Explain why the **triangles** are similar, then find BE and CD. Holt McDougal Geometry 7-3/

and the included side **of** one **triangle** are congruent to the corresponding parts **of** another **triangle**, the **triangles** are congruent. AAS If two angles and the non-included side **of** one **triangle** are congruent to the corresponding parts **of** another **triangle**, the **triangles** are congruent. HL If the hypotenuse and leg **of** one right **triangle** are congruent to the corresponding parts **of** another right **triangle**, the right **triangles** are congruent. Methods **of** Proving **Triangles** Congruent Using **Properties** **of** Right **triangles**

**Triangles** –A **triangle** is said to be inscribed in a circle if all **of** the vertices are points on the circle –Main **property**: if one **of** the sides is the diameter, the **triangle** IS a right **triangle**. Conversely, any inscribed right **triangle** has the diameter as one **of** its sides. –A right **triangle**/ at a point Quantitative Review Geometry – Lines and Angles –Exterior angles **of** a **triangle** a + b + c = 180; c + d = 180 d = a + b This **property** is frequently tested on GMAT –Parallel lines cut by a transversal: Sometimes/

CH. 4.1 APPLY **TRIANGLE** SUM **PROPERTIES** VOCAB Interior Angles : angles inside the **triangle** (sum = 180) Exterior Angles: angles outside the **triangle** Interior angles exterior angle exterior angle exterior angle CLASSIFYING BY SIDES SCALENEISOSCELES EQUILATERAL _____ CONGRUENT SIDES _____ CONGRUENT SIDES _____ / ACUTE ANGLES ACUTE _____ ACUTE ANGLES _____ ACUTE ANGLES RIGHT _____ ACUTE ANGLES 3 2 2 3 THEOREM 4.1: **TRIANGLE** SUM THEOREM The sum **of** the measures **of** the interior angles **of** a **triangle** is ________. CA B m

7-4 Applying **Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 2: Verifying Segments are Parallel Verify that. Since, by the Converse **of** the **Triangle** Proportionality Theorem. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Holt Geometry 7-4 Applying **Properties** **of** Similar **Triangles** Example 3: Art/

**Properties** **of** Special **Triangles** Objective: Write conjectures about isosceles **triangles** Isosceles **Triangle** Vertex angle legs base Base angles Construct an Isosceles **Triangle** Draw an angle, label it C Mark congruent segments along each side. Label A and B Connect A and B Measure and label base angles. Is there a pattern? A B Base angles Isosceles **Triangle** Conjecture If a **triangle** is isosceles, then ________________________ its base angles are/

to know. . . . . . about two **triangles** to prove that they are congruent? Corresponding Parts In Lesson 4.2, you learned that if all six pairs **of** corresponding parts (sides and angles) are congruent, then the **triangles** are congruent. B A C AB DE BC/) AAA ASA SSA SAS Name That Postulate SAS SAS SSA SAS Vertical Angles Reflexive **Property** (when possible) Vertical Angles Reflexive **Property** SAS SAS Vertical Angles Reflexive **Property** SSA SAS HW: Name That Postulate (when possible) HW: Name That Postulate (/

satisfy the above 4 **properties**: Bézier – **Properties** check at t=0: So, (**property** 1) Bézier – **Properties** check at t=1: So, (**property** 2) Note: Differentiation **of** the powers **of** t gives: Bézier – **Properties** check first derivative (gradient, velocity) at t: where Bézier – **Properties** check first derivative (/ a major shift to them Rendering Patches To have proper lighting we also need normals for the **triangles** We can simply use the **triangles** normal Or, if we want to be more accurate, we can use the actual normal to/

Answer - D Spring 2003 #39 G(f)(1) Similarity and the geometry **of** shape G(f)(1) Similarity and the geometry **of** shape. The student applies the concepts **of** similarity to justify **properties** **of** figures and solve problems. (C) In a variety **of** ways, the student [develops,] applies, and justifies **triangle** similarity relationships, such as right **triangle** ratios, [trigonometric ratios,] and Pythagorean triples. Correct Answer - H F 15/

3 Explain why ∆RSV ~ ∆RTU and then find RT. Step 1 Prove **triangles** are similar. It is given that S T. R R by Reflexive **Property** **of** . Therefore ∆RSV ~ ∆RTU by AA ~. Check It Out! Example 3/the Reflexive, Symmetric, and Transitive **Properties** **of** Equality have corresponding **properties** **of** congruence. These **properties** also hold true for similarity **of** **triangles**. Lesson Quiz 1. Explain why the **triangles** are similar and write a similarity statement. 2. Explain why the **triangles** are similar, then find BE and/

as well as the domain and range for both sin and cos functions before introducing another **property**: Period **Properties** **of** the Standard Sin and Cos Functions: Domain and Range; Period Period, Amplitude, Frequency WebsitePeriod,/**properties**. The website provides practice problems and solutions. Trig Applications Problems Inverse Trig Function Notation Website You have determined the length **of** a side **of** a **triangle** using the trig ratios and functions. Sometimes, we know the lengths **of** the sides **of** a **triangle**/

EXIT BACKNEXT Notice we can dissect this right **triangle**. We must rotate the first right **triangle** ¼ turn clockwise so the two **triangles** have the same alignment. EXIT BACKNEXT Since these **triangles** are similar, the following **properties** can be used. EXIT BACKNEXT It can /have EXIT BACKNEXT Example 2) EXIT BACKNEXT Example 3) EXIT BACKNEXT Example 4) EXIT BACKNEXT Summary EXIT BACKNEXT End **of** Right **Triangles** Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA 91754 Phone: (323) 265-8784 /

are congruent. In upcoming lessons, you will learn more efficient ways **of** proving that **triangles** are congruent. The **properties** below will be useful in such proofs. THEOREM A B C Theorem **Properties** **of** Congruent **Triangles** Reflexive **Property** **of** Congruent **Triangles** Every **triangle** is congruent to itself. D E F Symmetric **Property** **of** Congruent **Triangles** If , then . ABC DEF J K L Transitive **Property** **of** Congruent **Triangles** If and , then . JKL ABC DEF Goal 2 Classwork: p/

do you need to know... need to know...... about two **triangles** to prove that they are congruent? You learned that if all six pairs **of** corresponding parts (sides and angles) are congruent, then the **triangles** are congruent. Corresponding Parts ABC DEF B/That Postulate (when possible) ASA SAS AAA SSA Name That Postulate (when possible) SAS SAS SAS Reflexive **Property** Vertical Angles Reflexive **Property** SSA HW: Name That Postulate (when possible) HW: Name That Postulate Included Angle Included Side Hexagon vs/

angles and corresponding sides are congruent. THEOREM A B C Theorem 4.4 **Properties** **of** Congruent **Triangles** Reflexive **Property** **of** Congruent **Triangles** Every **triangle** is congruent to itself. D E F Symmetric **Property** **of** Congruent **Triangles** If , then . ABC DEF J K L Transitive **Property** **of** Congruent **Triangles** If and , then . JKL ABC DEF Goal 2 Using the SAS Congruence Postulate Prove that AEB DEC. 2 1 Statements Reasons AE DE, BE CE/

The Geometry **of** **Triangles**: Congruence, Similarity, and the Pythagorean Theorem The Geometry **of** **Triangles**: Congruence, Similarity, and the Pythagorean Theorem Congruent **Triangles** Similar **Triangles** The Pythagorean Theorem Congruent **Triangles** B E A D C F **Triangles** that are both the same size and same shape are called congruent **triangles**. B E A D C F The corresponding sides are congruent and corresponding angles have equal measures. Notation: Congruence **Properties** - SAS/

**Triangle** Congruence Postulates T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and **properties** **of** figures to find missing parts **of** geometric figures and provide logical justification LG.1.G.6 Give justification for conclusions reached by deductive reasoning Reflexive **property**: For every number a, a = a Transitive **property**: If a = b and b = c, then a = c Similarity: Two shapes are similar if corresponding/

CONGRUENT **TRIANGLES** **PROPERTIES** **OF** POLYGONS **PROPERTIES** **OF** QUADRILATERALS WHAT IS A CONGRUENT FIGURE? CORRESPONDING SIDES AND ANGLES ARE SAME MEASURE (CONGRUENT). CORRESPONDING IS SIMILAR TO MATCHING SIDES AND ANGLES. LOOK FOR TIC MARKS AND ANGLE ARCS, LOOK FOR ACTUAL SIDE MEASUREMENTS AND ANGLE MEASUREMENTS IF AVAILABLE. CONGRUENT **TRIANGLES** SSS: SIDE, SIDE, SIDE IF THREE SIDES **OF** ONE **TRIANGLE** ARE CONGRUENT TO THREE SIDES **OF** ANOTHER **TRIANGLE** THEN THE TWO **TRIANGLES** ARE/

angles equals 180º degrees. 60º 90º 30º + 60º 180º 30º 90º 40º 90º 40º 50º 180º 50º 90º **Property** **of** **triangles** The sum **of** all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 50º 90º 60º 60º 60º 180º **Property** **of** **triangles** 60º 60º 60º The sum **of** all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º What is the missing angle/

. Using CPCTC in proofs: We use CPCTC to prove that parts **of** a **triangle** are congruent. We MUST PROVE **TRIANGLES** ARE CONGRUENT FIRST! 1.USE one postulate to prove **triangles** are congruent. 2.What other information do I need? 3.What are the congruent **triangles**? 4.Use CPCTC STATEMENT REASON 1. Given 2. Reflexive **Property** 3. AAS 4. CPCTC *we’re proving congruent sides!!!!-use CPCTC/

. 4.2: Angle Relationships in **Triangles** The measure **of** one **of** the acute angles in a right **triangle** is 63.7°. What is the measure **of** the other acute angle? Statement Proof ∠A+∠B=90° Acute angles **of** a right **triangle** are complementary ∠A+∠63.7° =90° Substitution **property** ∠A =26.3° Subtraction **property** **of** equality The measure **of** one **of** the acute angles in a right **triangle** is 48 . What is the/

discovered that the sum **of** the two shorter sides **of** a **triangle** must be greater than the larger side – The **Triangle** inequality theorem. We also constructed **triangles** to discover that if two sides **of** a **triangle** are unequal then their opposite angles are unequal in the same order – **Triangle** Side and Angle Inequalities ( Theorem + Converse) Summary Theorems Exterior angles The **Properties** **of** the Inequalities Exterior Angle Theorem **Triangle** Side and Angle/

**Properties** **of** Equality Addition **Property** **of** Equality If a = b, then a + c = b + c. Subtraction **Property** **of** Equality If a = b, then a - c = b - c. Multiplication **Property** **of** Equality If a = b, then ac = bc. Division **Property** **of** Equality If a = b and c ≠ 0, then _a_ = _b_ . c c Algebraic **Properties** **of** Equality Reflexive **Property** **of** Equality a = a Symmetric **Property** **of**/it is, the more useful. Goals for today: Review **triangle** congruence ‘shortcuts’. Four **of** ‘em. Use all conjectures to prove examples on handouts /

supplementary If a quadrilateral is a parallelogram diagonals bisect each other each diagonal splits the parallelogram into two congruent **triangles**. http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/ http://www.ies.co.jp/math/products/geo1/applets/para/para.html Example 1: **Properties** **of** Parallelograms Def. **of** segs. Substitute 74 for DE. In CDEF, DE = 74 mm, DG = 31 mm, and m FCD = 42°. Find/

also need to be able to identify these shapes in a pattern block set). 4th Grade ▲ identify, name, describe and solve real world problems using the **properties** **of** geometric figures and their component parts (sides, angles): circle, **triangle**, square, rectangle, rhombus, trapezoid, hexagon, ellipse (oval), pentagon, octagon, polygon, quadrilateral, parallelogram, and regular and irregular polygons (figures should be recognized independently as well as/

, which determines X(v) and (X(v)). Summary and Open Problems Give distance approximation algorithms for all **properties** studied in [GR] (testing **of** bounded-degree graphs). With exception **of** **triangle**(subgraph)-freeness, complexity is polynomial in that **of** testing algorithms, and have only additive error. Can complexity **of** tri-free algorithm be improved? Can we decrease constant multiplicative factor in approximation? Sublinear distance approximation for bipartiteness/

Lesson 4-5: Isosceles and Equilateral **Triangles** Rigor: Use and apply **properties** **of** isosceles and equilateral **triangles** Relevance: **Triangle** **properties** are used in architecture, construction, and art. Concept Byte: paper folding conjectures (pg 265) If 2 sides have the same length, what is the relationship to the angles opposite the /

. Spitz Fall 2009 Objectives: Use **properties** **of** isosceles and equilateral **triangles** Use **properties** **of** right **triangles** Assignment: pp. 239-241 #1-26, 29-32, 33, 39 Using **properties** **of** Isosceles **Triangles** In lesson 4.1, you learned that a **triangle** is an isosceles if it has at least two congruent sides. If it has exactly two congruent sides, then they are the legs **of** the **triangle** and the non- congruent side is/

, income producing, upside potential with credit tenants, under market rental rates in great locations? Instead **of**: Over priced, empty / partially leased, under performing junk….. There are not any fire sales for good commercial **properties** 2007 Record Year for **Triangle** Real Estate Office Multi Family Retail Industrial Total Increase **of** 49% over 2006 $ 977M $ 991M $ 620M $ 483M $ 3,071B 2008 Outlook Debt market has changed/

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