A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted

Question

Mathematics

Janiya Madden

1 April, 01:33

A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted

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Luna Brady · Answer 1

From the figure we can express as Pythagoras theorem for rectangle triangles:

a^2 = r^2 + z^2

b^2 = r^2 + z^2

sen m = z/a

cos m = r/a

hence by the law of sines and cosines:

sen^2 m + cos^2 m = 1

(z/a) ^2 + (r/a) ^2 = 1

z^2/a^2 + r^2/a^2 = 1

substitue first equation value for a^2

z^2 / (r^2 + z^2) + r^2 / (r^2 + z^2) = 1

which proves that in fact is a triangle rectangle due to Pythagoras and sine-cosine laws, the same procedure can be follow for the other rectangle triangule in teh figure.