Everything Maths Grade 10

21

21

A

C

D B

O

SOLUTION

Step 1: Prove△ADC△ABC

In△ADCand△ABC:

AD =AB (given)

CD =CB (given)

AC (common side)

)△ADC △ABC (SSS)

)ADC^ =ABC^

Therefore one pair of opposite angles are equal in kiteABCD.

Step 2: Use properties of congruent triangles to proveACbisectsA^andC^

A^ 1 =A^ 2 (△ADC△ABC)

andC^ 1 =C^ 2 (△ADC△ABC)

Therefore diagonalACbisectsA^andC^.

We conclude that the diagonal between the equal sides of a kite bisects the two interior angles and is an axis

of symmetry.

Summary of the properties of a kite:
A

C

B D

• Diagonal between equal sides bisects the other diagonal.


• One pair of opposite angles are equal (the angles between unequal sides).


• Diagonal between equal sides bisects the interior angles and is an axis of symmetry.


• Diagonals intersect at 90 °

Chapter 7. Euclidean geometry 259