04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Solve for x.

1. x2 + 38 = 3x2 – 12

2. 137 + x = 180

3.

4. Find FE.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 2B: Using Properties of Kites

In kite ABCD, mDAB = 54°, and mCDF = 52°.

Find mABC.

Find mFDA.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.

If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 3A: Using Properties of Isosceles Trapezoids

Find mA.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 3B: Using Properties of Isosceles Trapezoids

KB = 21.9m and MF = 32.7. Find FB.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 4A: Applying Conditions for Isosceles Trapezoids

Find the value of a so that PQRS is isosceles.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 4

Find the value of x so that PQST is isosceles.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. The Trapezoid Midsegment Theorem is similar to the Triangle Midsegment Theorem.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 5: Finding Lengths Using Midsegments

Find EF.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Example 5

Find EH.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Lesson Review: Part II

Use the diagram for Items 4 and 5.

4. mWZY = 61°. Find mWXY.

5. XV = 4.6, and WY = 14.2. Find VZ.

6. Find LP.

04/19/23

Angle Relationships in TrianglesTrapezoids and Kites

Lesson Review: Part I

1. Erin is making a kite based on the pattern below. About how much binding does Erin need to cover the edges of the kite?

In kite HJKL, mKLP = 72°,and mHJP = 49.5°. Find eachmeasure.

2. mLHJ 3. mPKL