To discover, state and prove all about the diagonals and
Explanation of Solution
Given:
A convex kite
Concept used:
A kite is a quadrilateral that has two pairs of congruent sides, but opposite sides are not equal.
A kite
1. The diagonals of a kite are perpendicular.
Given:
Kite
To Prove:
Proof:
A kite has two distinct sets of congruent adjacent sides.
So,
Now, in
Hence, by Sid-Side-Side (SSS) congruency criteria
Now, in
Hence, by Sid-Angle-Side (SAS) congruency criteria
Now,
So,
Hence, diagonals of a kite are perpendicular to each other.
Hence proved.
2. The diagonal of a kite bisects the pair of opposite angles.
Given:
A kite
To prove:
Proof:
A kite has two distinct sets of congruent adjacent sides.
So,
Now, in
Hence, by Sid-Side-Side (SSS) congruency criteria
Therefore,
Hence proved.
Conclusion:
Diagonals are perpendicular to each other and bisects opposite angles.
Chapter 5 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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