The diagonals of a kite are perpendicular. For kite ⊥ RMNP, . In a kite, exactly one pair of opposite angles is congruent. ∠M ∠P. For kite RMNP, ≅ Example 1: If is a kite, find WXYZ m∠Z. The measures of ∠Y and ∠W are not congruent, so ∠X ∠Z. ≅ + + + = 360 m∠X m∠Y m∠Z m∠W + 60 + + 80 = 360 m∠X m∠Z + = 220 m∠X m∠Z = 110, = 110 m∠X m∠Z Example 2: If ABCD is a kite, find BC. The diagonals of a kite are perpendicular. Use the Pythagorean Theorem to find the missing length. + = + = 169 = 13 = BC Exercises If is a kite, find each measure. GHJK Find 1. m∠JRK. 2. If = 3 and = 10, find RJ RK JK. 3. If = 90 and = 110, find m∠GHJ m∠GKJ m∠HGK. 4. If = 7, find HJ HG. 5. If = 7 and = 5, find HG GR HR. 6. If = 52 and = 95, find m∠GHJ m∠GKJ m∠HGK.
The diagonals of a kite are perpendicular. For kite RMNP, ⊥ . In a kite, exactly one pair of opposite angles is congruent. For kite RMNP, ∠M ≅ ∠P. Example 1: If WXYZ is a kite, find m∠Z. The measures of ∠Y and ∠W are not congruent, so ∠X ≅ ∠Z. m∠X + m∠Y + m∠Z + m∠W = 360 m∠X + 60 + m∠Z + 80 = 360 m∠X + m∠Z = 220 m∠X = 110, m∠Z = 110 Example 2: If ABCD is a kite, find BC. The diagonals of a kite are perpendicular. Use the Pythagorean Theorem to find the missing length. + = + = 169 = 13 = BC Exercises If GHJK is a kite, find each measure. 1. Find m∠JRK. 2. If RJ = 3 and RK = 10, find JK. 3. If m∠GHJ = 90 and m∠GKJ = 110, find m∠HGK. 4. If HJ = 7, find HG. 5. If HG = 7 and GR = 5, find HR. 6. If m∠GHJ = 52 and m∠GKJ = 95, find m∠HGK.
6.6_np_kitestrapezoids.docx