Vocabulary trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid isosceles trapezoid midsegment of a trapezoid kite

TRAPEZOID Definition: 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 are two consecutive angles on a common base. Definition: If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

PROPERTY “OF” FOR OF & FOR

OF PROPERTIES: Trapezoid  Quad with EXACTLY 1 pair of opposite sides ║ Isosceles Trapezoid  legs  Isosceles Trapezoid  base  pairs  Isosceles Trapezoid  diags  FOR PROPERTIES: Quad with EXACTLY 1 pair of opposite sides ║  Trap Trap AND Legs  → Isos Trap Trap AND Diagonals  → Isos Trap Trap AND 1 base  pairs  → Isos Trap

Using Properties of Isosceles Trapezoids Reflexive Isos. trap.  base s  KFJ  MJF Isos. trap.  legs  ∆FKJ  ∆JMF SAS In an isosceles trapezoid corresponding parts of the congruent diagonals are congruent. BKF  BMJ CPCTC FBK  JBM Vert. s  ∆FBK  ∆JBM AAS CPCTC

Check It Out! Example 3a Find mF. mF + mE = 180° Same-Side Int. s Thm. E  H Isos. trap. s base  mE = mH Def. of  s mF + 49° = 180° Substitute 49 for mE. mF = 131° Simplify. In an isosceles trapezoid opposite base angles are supplementary

Example 4A: Applying Conditions for Isosceles Trapezoids Find the value of a so that PQRS is isosceles.

The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it. ll to the bases Average of the bases

Example 5: Finding Lengths Using Midsegments Find EF. Find EH.

Definition: A kite is a quadrilateral with exactly two pairs of congruent consecutive sides (opposite sides not ).

PROPERTIES “OF” One diagonal perpendicularly bisects the other

Kite  Quad with exactly 2 pair ≅ consecutive sides Kite → diagonals ⊥ Kite → Exactly 1 pair opposite angles ≅

Example 2A: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD and mABC.

Check It Out! Example 2a In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT and mQPS.

Lesson Quiz: 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, mKLP = 72°, and mHJP = 49.5°. Find each measure. 2. mLHJ 3. mPKL

Lesson Quiz: Part II Use the diagram for Items 4 and 5. 4. mWZY = 61°. Find mWXY. 5. XV = 4.6, and WY = 14.2. Find VZ. 6. Find LP.