Geometry Mini-Lesson AB || DC and AD || BC

Slides:

Advertisements

Similar presentations

6.4 Rhombuses, Rectangles, and Squares

Advertisements

6.3/4 Rhombuses, Rectangles, and Squares. Three Definitions 1.A rhombus is a parallelogram with four congruent sides. 1.A rectangle is a parallelogram.

Parallelogram A quadrilateral with both pairs of opposite sides parallel *opposite sides are congruent *opposite angles are congruent *diagonals bisect.

Quadrilateral Venn Diagram

Unit 3 Special Quadrilaterals

What quadrilateral am I? Use the given properties to decide what type of quadrilateral is being described. Continue.

Special Quadrilaterals

6-3 Proving That a Quadrilateral Is a Parallelogram

Quadrilateral Proofs.

3 Special Figures: The Rhombus, The Rectangle, The Square A Retrospect.

Properties of Quadrilaterals

*Quadrilateral I have exactly four sides and angles. If you add all of my angles together, then you would have

For each, attempt to create a counter example or find the shape is MUST be….. Quadrilateral Properties.

Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram.

Proof Geometry.  All quadrilaterals have four sides.  They also have four angles.  The sum of the four angles totals 360°.  These properties are.

6.4 Rhombuses, Rectangles, and Squares Day 4 Review  Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 °

Warm-Up ABCD is a parallelogram. Find the length of BC. A B C D 5x + 3 3x + 11.

2/9/15 Unit 8 Polygons and Quadrilaterals Special Parallelograms

Bell Ringer Lesson 6-4: Rhombus & Square 1. 2 Rhombi Rectangles & Squares.

WARM UP—find your new seat * TAKE OUT your homework ** Review for a quiz—5 min silent.

Aim: what are the properties of quadrilaterals? Do Now: Name 2 ways to identify a parallelogram as a square 1.A rectangle with 1 pair of consecutive congruent.

Parallelograms have Properties Click to view What is a parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Rhombuses, Rectangles, and Squares

Special Parallelograms

Rhombus 1.Both pairs of opposite sides are parallel 2. Both pairs of opposite sides are congruent 3. Both pairs of opposite angles are congruent 4. Consecutive.

8.5 Rhombi and Squares What you’ll learn:

Geometry 6-4 Rhombus Opposite sides parallel? Opposite sides congruent? Opposite angles congruent? Consecutive angles supplementary? Diagonals congruent?

Geometry 6-4 Properties of Rhombuses, Rectangles, and Squares.

Proofs with Quadrilaterals. Proving Quadrilaterals are Parallelograms Show that opposite sides are parallel by same slope. Show that both pairs of opposite.

 Rhombus – a parallelogram with four congruent sides.  Rectangle – a parallelogram with four right angles.

6-4 Properties of Rhombuses, Rectangles, and Squares

EXAMPLE 3 List properties of special parallelograms

7.2/7.3 Parallelograms! Learning Objective: to identify and classify parallelograms and prove that figures are special types of parallelograms. Warm-up.

Properties of Rhombuses, Rectangles, and Squares Lesson 8.4.

A D B C Definition: Opposite Sides are parallel.

Geometry SECTION 6: QUADRILATERALS. Properties of Parallelograms.

Lesson 6-4: Rhombus & Square

7.2 Parallelograms. Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles Opposite angles.

Special Quadrilaterals. KITE  Exactly 2 distinct pairs of adjacent congruent sides  Diagonals are perpendicular  Angles a are congruent.

Parallelograms Properties & Attributes. Parallelograms …are quadrilaterals in which both pairs of opposite sides are parallel If a quadrilateral is a.

7.4 Properties of Special Parallelograms OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

Lesson: Objectives: 6.5 Squares & Rhombi  To Identify the PROPERTIES of SQUARES and RHOMBI  To use the Squares and Rhombi Properties to SOLVE Problems.

 6.3 Showing Quadrilaterals are Parallelograms. We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms  What 5 facts are ALWAYS.

Interior and exterior angles. Exterior and interior angles are supplementary.

 Parallelograms are quadrilaterals, this means they have 4 sides.

7/1/ : Properties of Quadrilaterals Objectives: a. Define quadrilateral, parallelogram, rhombus, rectangle, square and trapezoid. b. Identify the.

Do-Now 1)Find x. 2) Find x. 4x + 1 3x + 1 2x x 2x – 10 x 2 – 2x – 69.

Warm Up:  Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving?  What is the measure of CD? 

Warm-Up ABCD is a parallelogram. AB = 12 and BC = 25

6.4 EQ: What properties do we use to identify special types of parallelograms?

Unit 2 – Similarity, Congruence, and Proofs

Properties of Parallelograms

Parallelograms.

Polygons – Parallelograms

Lesson 6-4: Rhombus & Square

Lecture 6-4 Rhombi and Squares.

6-5 Conditions for Rhombuses, Rectangles, and Squares

Parallelogram Definition: A quadrilateral with two pairs of parallel sides. Picture: Marked parallel and congruent.

Parallelogram Rectangle Rhombus Square Trapezoid Kite

Section 5-1 Parallelograms.

Six Properties of Parallelograms

8.4 Properties of Rhombuses, Rectangles, and Squares

Properties of Special Parallelograms

Lesson 6-4: Rhombus & Square

Lesson 61 Determining if a Quadrilateral is a Parallelogram

Lesson 6-4: Rhombus & Square

6.3 Conditions for Parallelograms

Properties of Parallelograms

6.3 Proving Quadrilaterals and Parallelograms

Presentation transcript:

Geometry Mini-Lesson AB || DC and AD || BC Given quadrilateral ABCD, which of the following sufficiently indicates that the quadrilateral is a rectangle? AB || DC and AD || BC AB is congruent to DC, and AD is congruent to BC A and C are right angles AB is congruent to DC, and AB || DC, and B is a right angle MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson Which statement is FALSE? Every square is a rhombus. All rectangles are parallelograms. The diagonals of all parallelograms bisect each other. Every property of a square is also a property of a parallelogram. MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson All sides of a rhombus are congruent. Figure JKLM is a rhombus. The measure of angle JKM is (2x + 17)° and the measure of angle LKM is (3x − 19)°. Which statement best explains why the equation 2x + 17 = 3x − 19 can be used to find x? All sides of a rhombus are congruent. Opposite angles in a rhombus are congruent. The diagonals of a rhombus are perpendicular. The diagonals of a rhombus bisect opposite angles. MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson Jasmine is about to buy a rectangular plot of land to build her house. Before she buys it, she wants to verify the shape is truly rectangular. Which of the following methods should she use to prove the plot of land is a rectangle? Verify that the diagonals of the plot of land are congruent. Verify that opposite sides of the plot of land are congruent. Verify that the diagonals of the plot of land bisect each other. Verify that consecutive angles of the plot of land are supplementary. MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson Given a rhombus, which statement is FALSE? The diagonals are perpendicular. The diagonals bisect each other. Exactly one pair of opposite sides is parallel. Both pairs of opposite angles are congruent. MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson Figure STUV is a parallelogram. The measure of angle S is (5x + 13)° and the measure of angle T is (7x − 40)°. Which statement best explains why the equation 5x + 13 + 7x − 40 = 180 can be used to find x? Opposite sides of a parallelogram are parallel. Opposite angles in a parallelogram are congruent. Consecutive angles in a parallelogram are supplementary. Consecutive angles in a parallelogram are complementary. MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson Miguel thinks the shape of his math classroom is a square. Tom disagrees. He thinks the classroom is rectangular but not square. Which of the following methods should Miguel use to prove his rectangular math classroom is truly square? Verify the diagonals of the classroom are perpendicular. Verify that opposite sides in the classroom are congruent. Verify that the diagonals of the classroom are congruent. Verify that the diagonals of the classroom bisect each other. MA.912.G.3.4: Prove theorems involving quadrilaterals.