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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
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
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
Example 5: Finding Lengths Using Midsegments
Find EF.
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.