# 5.3 Investigations 1

Author:
diego83720

## What Are Some Properties of Kites?

Step 1: On patty paper,, draw two connected segments of different lengths as shown. Fold though the end points and trace the two segments on the back of the patty paper. Step 2: Compare the size of each pair of opposite angles in your kite by folding an angle onto the opposite angle. Are the vertex angles congruent? Are the nonvertex angles congruent? Share your observation with others near you and complete the conjecture. The vertex angles are not congruent however the nonvertex angles are congruent. Kite Angles Conjecture  The nonvertex angles of a kite are congruent Step 3: Draw the diagonals. How are the diagonals related? Share your observation with others in your group and complete the conjecture. The diagonals are related because when they intersect, they form right angles Kite Diagonals Conjecture The diagonals of a kite are perpendicular to each other. What else seems to be true about the diagonals of kites? Another aspect that seems to be true about the diagonals of kites is that the distance from the top vertex point to where the diagonal intersect has the same distance as the nonvertex angle to where it also intersects Step 4: Complete the lengths of the segment on both diagonals. Does either diagonal bisect the other? Share your observations with others near you. Copy and complete the conjecture. Yes the diagonal from the vertex angle bisects the diagonal from the nonvertex angles and would also form right angles which would make it the perpendicular bisector Kite Diagonal Bisector Conjecture The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal. Step 5: Fold along both diagonals. Does either diagonal bisect any angles? Share your observations with others and complete the conjecture. Yes, the diagonal bisect the vertex angles Kite Angles Bisector Conjecture The vertex angles of a kite are bisected by a diagonal.