Five-Minute Check (over Lesson 2-6) Main Ideas Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate Example 1: Proof With Segment Addition Theorem 2.2: Segment Congruence Example 2: Proof with Segment Congruence Lesson 7 Menu

Write proofs involving segment addition. Write proofs involving segment congruence. Lesson 7 MI/Vocab

Lesson 7 PS1

Lesson 7 PS2

Proof with Segment Addition Prove the following. Given: PR = QS Prove: PQ = RS Proof: Statements Reasons 1. Given PR = QS 1. 2. Subtraction Property PR – QR = QS – QR 2. 3. Segment Addition Postulate PR – QR = PQ; QS – QR = RS 3. 4. Substitution PQ = RS 4. Lesson 7 Ex1

Given: AC = AB AB = BX CY = XD Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD Lesson 7 CYP1

Which choice correctly completes the proof? 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition Property AC + CY = BX + XD 4. AY = BD 6. Substitution 6. Proof: Statements Reasons Which choice correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ? Lesson 7 CYP1

C. Definition of congruent symbols A. Addition Property B. Substitution C. Definition of congruent symbols D. Segment Addition Postulate A B C D Lesson 7 CYP1

Lesson 7 TH1

Proof with Segment Congruence Prove the following. Given: Prove: Lesson 7 Ex2

Proof with Segment Congruence Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. Given 3. 4. Transitive Property 4. 5. Symmetric Property 5. Lesson 7 Ex2

Prove the following. Given: Prove: Lesson 7 CYP2

Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ? Lesson 7 CYP2

C. Segment Addition Postulate A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property A B C D Lesson 7 CYP2

End of Lesson 7

Five-Minute Checks Image Bank Math Tools Conditional Statements Patterns and Proofs CR Menu

Lesson 2-1 (over Chapter 1) Lesson 2-2 (over Lesson 2-1) 5Min Menu

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Animation 1

Refer to the figure. Identify the solid. (over Chapter 1) Refer to the figure. Identify the solid. A. triangular pyramid B. triangular prism C. rectangular pyramid D. cone A B C D 5Min 1-1

Find the distance between A(–3, 7) and B(1, 4). (over Chapter 1) Find the distance between A(–3, 7) and B(1, 4). A. 3.61 B. 4 C. 5 D. 11.70 A B C D 5Min 1-2

(over Chapter 1) Find mC if C and D are supplementary, mC = 3y – 5, and mD = 8y + 20. A. 15 B. 40 C. 45 D. 140 A B C D 5Min 1-3

Find SR if R is the midpoint of SU shown in the figure. (over Chapter 1) Find SR if R is the midpoint of SU shown in the figure. A. 3 B. 10 C. 22 D. 24 A B C D 5Min 1-4

Find n if bisects VWY shown in the figure. (over Chapter 1) Find n if bisects VWY shown in the figure. A. 10 B. 8 C. 5 D. 3 A B C D 5Min 1-5

Find the coordinates of the midpoint of MN if M(3, 6) and N(9, –4). (over Chapter 1) Find the coordinates of the midpoint of MN if M(3, 6) and N(9, –4). A. (12, 2) B. (6, 5) C. (1, 6) D. (6, 1) A B C D 5Min 1-6

(over Lesson 2-1) Make a conjecture about the next item in the sequence: 1, 4, 9, 16, 25. A. 28 B. 30 C. 36 D. 50 A B C D 5Min 2-1

Make a conjecture about the next item in the sequence: (over Lesson 2-1) Make a conjecture about the next item in the sequence: A. B. C. D. A B C D 5Min 2-2

(over Lesson 2-1) In ΔABC, if mA = 60, mB = 60, and mC = 60, then ΔABC is an equilateral triangle. Is the conjecture true or false? Give a counterexample for any false conjecture. A. true B. false; AB  BC A B 5Min 2-3

(over Lesson 2-1) If 1 and 2 are supplementary angles, then 1 is congruent to 2. Is the conjecture true or false? Give a counterexample for any false conjecture. A. true B. false; m1 = 70 and m2 = 110 A B 5Min 2-4

(over Lesson 2-1) If ΔRST is isosceles, then RS is congruent to ST. Is the conjecture true or false? Give a counterexample for any false conjecture. A. true B. false; A B 5Min 2-5

(over Lesson 2-1) Make a conjecture about the next item in the sequence: 64, –32, 16, –8, 4. A. –4 B. –2 C. 2 D. 4 A B C D 5Min 2-6

A. True; 12 + (–4) = 8, and a triangle has four sides. (over Lesson 2-2) Which choice shows a compound statement for the conjunction p and r, and also states its truth value? p: 12 + (–4) = 8. r: A triangle has four sides. A. True; 12 + (–4) = 8, and a triangle has four sides. B. True; 12 + (–4)  8, and a triangle has four sides. C. False; 12 + (–4) = 8, and a triangle has four sides. D. False; 12 + (–4)  8, and a triangle has four sides. A B C D 5Min 3-1

(over Lesson 2-2) Which choice shows a compound statement for the disjunction q or r, and also states its truth value? q: A right angle measures 90 degrees. r: A triangle has four sides. A. True; a right angle measures 90 degrees, or a triangle has four sides. B. True; a right angle measures 90 degrees, or a triangle does not have four sides. C. False; a right angle does not measure 90 degrees, or a triangle has four sides. D. False; a right angle measures 90 degrees, or a triangle has four sides. A B C D 5Min 3-2

A. True; 12 + (–4) = 8, or a triangle has four sides. (over Lesson 2-2) Which choice shows a compound statement for the disjunction ~p or r, and also states its truth value. p: 12 + (–4) = 8. r: A triangle has four sides. A. True; 12 + (–4) = 8, or a triangle has four sides. B. True; 12 + (–4)  8, or a triangle has four sides. C. False; 12 + (–4)  8, or a triangle does not have four sides. D. False; 12 + (–4)  8, or a triangle has four sides. A B C D 5Min 3-3

(over Lesson 2-2) Which choice shows a compound statement for the conjunction q and ~r, and also states its truth value? q: A right angle measures 90 degrees. r: A triangle as four sides. A. True; a right angle does not measure 90 degrees or a triangle has four sides. B. True; a right angle measures 90 degrees and a triangle does not have four sides. C. False; a right angle does not measure 90 degrees and a triangle does not have four sides. D. False; a right angle does not measure 90 degrees and a triangle has four sides. A B C D 5Min 3-4

(over Lesson 2-2) Which choice shows a compound statement for the disjunction ~p or ~q, and also states its truth values? p: 12 + (–4) = 8. q: A right angle measures 90 degrees. A. True; 12 + (–4) = 8, or a right angle measures 90 degrees. B. True; 12 + (–4)  8, or a right angle does not measure 90 degrees. C. False; 12 + (–4) = 8, or a right angle measures 90 degrees. D. False; 12 + (–4)  8, or a right angle does not measure 90 degrees. A B C D 5Min 3-5

(over Lesson 2-2) Given the following statements which compound statement is false? s: Triangles have three sides. q: 5 + 3 = 8. A. s or q B. s and q C. ~s and ~q D. ~s or q A B C D 5Min 3-6

Identify the hypothesis and conclusion: If 6x – 5 = 19, then x = 4. (over Lesson 2-3) Identify the hypothesis and conclusion: If 6x – 5 = 19, then x = 4. A. Hypothesis: 6x – 5 = 19; Conclusion: x = 4 B. Hypothesis: 6x – 5 = 19 Conclusion: x  4 C. Hypothesis: x = 4 Conclusion: 6x – 5 = 19 D. Hypothesis: 6x – 5  19 Conclusion: x = 4 A B C D 5Min 4-1

(over Lesson 2-3) Identify the hypothesis and conclusion: A polygon is a hexagon if it has six sides. A. Hypothesis: the polygon is not a hexagon Conclusion: a polygon has six sides B. Hypothesis: the polygon is a hexagon Conclusion: a polygon has six sides C. Hypothesis: a polygon has six sides Conclusion: the polygon is a hexagon D. Hypothesis: a polygon does not have six sides Conclusion: the polygon is a hexagon A B C D 5Min 4-2

A. If you are healthy, then you must exercise. (over Lesson 2-3) Which choice shows the statement in if-then form? Exercise makes you healthier. A. If you are healthy, then you must exercise. B. If you are not healthy, then you must exercise. C. You will not be healthy if you do not exercise. D. If you exercise, then you will be healthier. A B C D 5Min 4-3

A. If a figure has 4 sides, then it is a square. (over Lesson 2-3) Which choice shows the statement in if-then form? Squares have 4 sides. A. If a figure has 4 sides, then it is a square. B. If a figure is a square, then it has 4 sides. C. A figure is not a square if it does not have 4 sides. D. If a figure is not a square, then it does not have 4 sides. A B C D 5Min 4-4

A. If A is a right angle, then mA = 90. (over Lesson 2-3) Which statement represents the inverse of the statement If A is a right angle, then mA = 90? A. If A is a right angle, then mA = 90. B. If mA = 90, then A is a right angle. C. If A is not a right angle, then mA  90. D. If mA  90, then A is not a right angle. A B C D 5Min 4-5

(over Lesson 2-4) Determine whether the stated conclusion is valid based on the given information. If not, choose invalid. Given: A and B are supplementary. Conclusion: mA + mB = 180 A. valid B. invalid A B 5Min 5-1

(over Lesson 2-4) Determine whether the stated conclusion is valid based on the given information. If not, choose invalid. Given: Polygon RSTU is a quadrilateral. Conclusion: Polygon RSTU is a square. A. valid B. invalid A B 5Min 5-2

(over Lesson 2-4) Determine whether the stated conclusion is valid based on the given information. If not, choose invalid. Given: ΔABC is isosceles. Conclusion: ΔABC has at least two congruent sides. A. valid B. invalid A B 5Min 5-3

(over Lesson 2-4) Determine whether the stated conclusion is valid based on the given information. If not, choose invalid. Given: A and B are congruent. Conclusion: A and B are vertical. A. valid B. invalid A B 5Min 5-4

(over Lesson 2-4) Determine whether the stated conclusion is valid based on the given information. If not, choose invalid. Given: mY in ΔWXY = 90. Conclusion: ΔWXY is a right triangle. A. valid B. invalid A B 5Min 5-5

(over Lesson 2-4) Which is a valid conclusion for the statement R and S are vertical angles? A. mR + mS = 180 B. mR + mS = 90 C. R and S are adjacent. D. R is congruent to S. A B C D 5Min 5-6

A. A line contains at least two points. (over Lesson 2-5) In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that A, B, and C are collinear? A. A line contains at least two points. B. A line contains only two points. C. A line contains at least three points. D. A line contains only three points. A B C D 5Min 6-1

(over Lesson 2-5) In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that lies in plane R? A. Through two points, there is exactly one line in a plane. B. Any plane contains an infinite number of lines. C. Through any two points on the same line, there is exactly one plane. D. If two points lie in a plane, then the entire line containing those points lies in that plane. A B C D 5Min 6-2

(over Lesson 2-5) In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that A, H, and D are coplanar? A. Through any two points on the same line, there is exactly one plane. B. Through any three points not on the same line, there is exactly one plane. C. If two points lie in a plane, then the entire line containing those points lies in that plane. D. If two lines intersect, then their intersection lies in exactly one plane. A B C D 5Min 6-3

(over Lesson 2-5) In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that E and F are collinear? A. Through any two points, there is exactly one line. B. A line contains only two points. C. If two points lie in a plane, then the entire line containing those points lies in that plane. D. Through any two points, there are many lines. A B C D 5Min 6-4

(over Lesson 2-5) In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that intersects at point B? A. The intersection point of two lines lies on a third line, not in the same plane. B. If two lines intersect, then their intersection point lies in the same plane. C. The intersection of two lines does not lie in the same plane. D. If two lines intersect, then their intersection is exactly one point. A B C D 5Min 6-5

Which statement is not supported by a postulate? (over Lesson 2-5) Which statement is not supported by a postulate? A. R and S are collinear. B. M lies on . C. P, X, and Y must be collinear. D. J, K, and L are collinear. A B C D 5Min 6-6

A. Distributive Property B. Addition Property C. Substitution Property (over Lesson 2-6) State the property that justifies the statement: 2(LM + NO) = 2LM + 2NO. A. Distributive Property B. Addition Property C. Substitution Property D. Multiplication Property A B C D 5Min 7-1

A. Distributive Property B. Substitution Property C. Addition Property (over Lesson 2-6) State the property that justifies the statement: If mR = mS, then mR + mT = mS + mT. A. Distributive Property B. Substitution Property C. Addition Property D. Transitive Property A B C D 5Min 7-2

A. Multiplication Property B. Division Property (over Lesson 2-6) State the property that justifies the statement: If 2PQ = OQ, then PQ = A. Multiplication Property B. Division Property C. Distributive Property D. Substitution Property A B C D 5Min 7-3

State the property that justifies the statement: mZ = mZ. (over Lesson 2-6) State the property that justifies the statement: mZ = mZ. A. Reflexive Property B. Symmetric Property C. Transitive Property D. Substitution Property A B C D 5Min 7-4

C. Substitution Property D. Transitive Property (over Lesson 2-6) State the property that justifies the statement: If BC = CD and CD = EF, then BC = EF. A. Reflexive Property B. Symmetric Property C. Substitution Property D. Transitive Property A B C D 5Min 7-5

Which property justifies the statement: If 90 = mI, then mI = 90? (over Lesson 2-6) Which property justifies the statement: If 90 = mI, then mI = 90? A. Substitution Property B. Reflexive Property C. Symmetric Property D. Transitive Property A B C D 5Min 7-6

A. Substitution Property B. Reflexive Property C. Symmetric Property (over Lesson 2-7) Justify the statement with a property of equality or a property of congruence: If AB  CD and CD  EF, then AB  EF. A. Substitution Property B. Reflexive Property C. Symmetric Property D. Transitive Property A B C D 5Min 8-1

A. Substitution Property B. Reflexive Property C. Symmetric Property (over Lesson 2-7) Justify the statement with a property of equality or a property of congruence: RS  RS. A. Substitution Property B. Reflexive Property C. Symmetric Property D. Transitive Property A B C D 5Min 8-2

A. Segment Addition Postulate B. Addition Postulate (over Lesson 2-7) Justify the statement with a property of equality or a property of congruence: If H is between G and I, then GH + HI = GI. A. Segment Addition Postulate B. Addition Postulate C. Distributive Property D. Substitution Property A B C D 5Min 8-3

(over Lesson 2-7) State the conclusion that can drawn from the statement using the Segment Addition Postulate: W is between X and Z. A. XW = WZ B. XW > XZ C. XZ + WZ = XW D. XW + WZ = XZ A B C D 5Min 8-4

(over Lesson 2-7) State the conclusion that can be drawn from the statement using the Transitive Property of Congruence: LM  NO, and NO  PQ. A. PQ  NO. B. NO  LM. C. LM  PQ. D. LM  LM. A B C D 5Min 8-5

Which statement is true, given that K is between J and L? (over Lesson 2-7) Which statement is true, given that K is between J and L? A. JK + KL = JL B. JL + LK = JK C. LJ + JK = LK D. JK  KL A B C D 5Min 8-6

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