Crazy Math

Let us learn how learn geometry angle proof online geometry tutoring:

A parallelogram is a rhombus if its diagonals are 90°.

Given Data: ABCD is a parallelogram where the diagonals are AC and BD are perpendicular.

To prove: ABCD is a rhombus.

To find online geometry problems

Construction: Draw the diagonals AC and BD. Let M be the intersection point of AC and BD (see Figure).

Proof: In triangles AMB and BMC,

(i) ∠AMB = ∠BMC = 90°
(ii) AM = MC
(iii) BM is common.

By SSA criterion, ΔAMB ≡ ΔBMC.

Corresponding sides are equal. In particular, AB = BC.

Since ABCD is a parallelogram, AB = CD, BC = AD.

AB = BC = CD = AD.

Hence ABCD is a rhombus. The theorem is proved.

Need online geometry homework help