Lesson 8-6 Trapezoids Theorem 8.18

Slides:

Advertisements

Similar presentations

Advertisements

8.3 Tests for Parallelograms

Trapezoids Chapter 6.6. TrapezoidDef: A Quadrilateral with exactly one pair of parallel sides.  The parallel sides are called the bases.  The non-parallel.

8.6 Trapezoids.

Sect. 6.5 Trapezoids and Kites Goal 1 Using Properties of Trapezoids Goal 2 Using Properties of Kites.

CP Geometry Mr. Gallo. What is a Trapezoid Trapezoid Isosceles Trapezoid leg Base Base Angles leg Base Angles If a quadrilateral is a trapezoid, _________________.

6.6 Trapezoids and Kites A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases. The.

Trapezoids and Kites Chapter 6 Section 6 Tr.

6-6 Trapezoids and Kites.

Trapezoids and Kites Section 8.5.

Quadrilateral Proofs.

Welcome to Interactive Chalkboard

QuadrilateralsQuadrilaterals 5-2. EXAMPLE 1 Solve a real-world problem Ride An amusement park ride has a moving platform attached to four swinging arms.

Direct Analytic Proofs. If you are asked to prove Suggestions of how to do this Two lines parallel Use the slope formula twice. Determine that the slopes.

Advanced Geometry Polygons Lesson 4

OBJECTIVE: PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM

Proof using distance, midpoint, and slope

Tests for Parallelograms Advanced Geometry Polygons Lesson 3.

Section 16.1 Pythagorean Theorem a=11.6. x=3.86 y=4.60 x=

8.5 Trapezoids.

Tests for Parallelograms

6-6 Trapezoids and Kites You used properties of special parallelograms. Apply properties of trapezoids. Apply properties of kites.

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

5.11 Use Properties of Trapezoids and Kites. Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg.

5.11Properties of Trapezoids and Kites Example 1 Use a coordinate plane Show that CDEF is a trapezoid. Solution Compare the slopes of the opposite sides.

Geometry Section 8.5 Use Properties of Trapezoids and Kites.

Trapezoids & Kites Sec 6.5 GOALS: To use properties of trapezoids and kites.

You used properties of special parallelograms.

Lesson 8-6 Trapezoids.

1 Lesson 6-6 Trapezoids and Kites. 2 Trapezoid A quadrilateral with exactly one pair of parallel sides. Definition: Base Leg/ Height Isosceles trapezoid.

Geometry Section 6.5 Trapezoids and Kites. A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel. The sides that are parallel.

6-6 Trapezoids and Kites Objective: To verify and use properties of trapezoids and kites.

6.5: TRAPEZOIDS AND KITES OBJECTIVE: TO VERIFY AND USE PROPERTIES OF TRAPEZOIDS AND KITES.

Friday, November 30, 2012 Agenda: TISK, No MM Upcoming Important Dates Solve problems using properties of trapezoids and kites. Homework: No HW – Project.

Proving Properties of Special Quadrilaterals

Trapezoids April 29, 2008.

Chapter 6: Quadrilaterals

6.3 TESTS FOR PARALLELOGRAMS. If… Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent Both pairs of opposite angles are.

Tests for Parallelograms

8.4 Rectangles. Objectives  Recognize and apply properties of rectangles  Determine whether parallelograms are rectangles.

A QUADRALATERAL WITH BOTH PAIRS OF OPPOSITE SIDES PARALLEL

Ch 8 test Things I would know. How to name consecutive angles/vertices/sides Or Non consecutive angles/vertices/sides.

Lesson 2.17: Trapezoid & Kites 1 Lesson 6-5 Trapezoids and Kites.

Chapter 6 Lesson 1 Objective: To define and classify special types of quadrilaterals.

Trapezoids Euclidean Geometry High School Math Online.

Geometry 6.3 I can recognize the conditions that ensure a quadrilateral is a parallelogram.

In the figure, LMNO is a rhombus. Find x. Find y.

8.5 – Use Properties of Trapezoids and Kites. Trapezoid: Consecutive interior angles are supplementary A B C D m  A + m  D = 180° m  B + m  C = 180°

Use Properties of Trapezoids and Kites Lesson 8.5.

Trapezoids Section 6.5. Objectives Use properties of trapezoids.

TRAPEZOIDS AND KITES Lesson 6-6. VOCABULARY: Trapezoid: A quadrilateral with exactly one pair of parallel sides. Bases: The parallel sides of a trapezoid.

Section 6-5 Trapezoids and Kites. Trapezoid A quadrilateral with exactly one pair of parallel sides.

Trapezoids Trapezoid - A quadrilateral with exactly one pair of parallel sides. Bases - The parallel sides of a trapezoid. Legs - The nonparallel sides.

Aim: How can we solve coordinate quadrilateral proofs

Trapezoids and Kites Section 7.5.

6-6 Trapezoids & Kites The student will be able to:

Classifying Quadrilaterals

Trapezoids One pair of parallel sides. (called Base)

LESSON 6–6 Trapezoids and Kites.

6-1 Classifying Quadrilaterals

Properties of Trapezoids and Kites

Lesson 8.5: Properties of Trapezoids and Kites

Properties of Trapezoids and Kites

Lesson: 6.6 Trapezoids Objectives:

PROVING A QUADRILATERAL IS AN ISOSCELES TRAPEZOID

Fill in the following table – checking each characteristic that applies to the figures listed across the top; Characteristic Polygon Quadrilateral Parallelogram.

6.3 Proving Quadrilaterals are Parallelograms

4.4 The Trapezoid A quadrilateral with exactly two parallel sides. The parallel sides are called the bases and the nonparallel sides are the legs. Median.

Presentation transcript:

Lesson 8-6 Trapezoids Theorem 8.18 Both pairs of base angles of an isosceles trapezoid are congruent Theorem 8.19 The diagonals of an isosceles trapezoid are congruent. Theorem 8.20 The median of a trapezoid is parallel to the bases and its measure is one-half the sum of the measures of the bases.

Given: KLMN is an isosceles trapezoid. Write a flow proof. Given: KLMN is an isosceles trapezoid. Prove: Example 6-1a

Proof: Example 6-1a

Given: ABCD is an isosceles trapezoid. Write a flow proof. Given: ABCD is an isosceles trapezoid. Prove: Example 6-1b

Proof: Example 6-1b

Answer: Both trapezoids are isosceles. The top of this work station appears to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Each pair of base angles is congruent, so the legs are the same length. Answer: Both trapezoids are isosceles. Example 6-2a

The sides of a picture frame appear to be two adjacent trapezoids The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Answer: yes Example 6-2b

ABCD is a quadrilateral with vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Verify that ABCD is a trapezoid. A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula. Example 6-3a

slope of slope of slope of slope of Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid. Example 6-3b

ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain. Example 6-3c

First use the Distance Formula to show that the legs are congruent. Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid. Example 6-3d

a. Verify that QRST is a trapezoid. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). a. Verify that QRST is a trapezoid. Answer: Exactly one pair of opposite sides is parallel. Therefore, QRST is a trapezoid. b. Determine whether QRST is an isosceles trapezoid. Explain. Answer: Since the legs are not congruent, QRST is not an isosceles trapezoid. Example 6-3e

DEFG is an isosceles trapezoid with median Find DG if and Example 6-4a

Subtract 20 from each side. Theorem 8.20 Substitution Multiply each side by 2. Subtract 20 from each side. Answer: Example 6-4b

DEFG is an isosceles trapezoid with median Find , and if and Because this is an isosceles trapezoid, Example 6-4c

Consecutive Interior Angles Theorem Substitution Combine like terms. Divide each side by 9. Answer: Because Example 6-4d

WXYZ is an isosceles trapezoid with median b. Answer: Answer: Because Example 6-4e