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Chapter 5: Q35 (page 194)

Prove that if the diagonals of parallelograms are congruent, then the parallelogram is a rectangle.

Short Answer

Expert verified

If the diagonals of parallelograms are congruent, then the parallelogram is a rectangle.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

The CPCTC theorem states that when two triangles are congruent, then every corresponding part of one triangle is congruent to the other.

03

Step 3. Step description.

From the figure, ΔABCand ΔABD.

AB=AB (Sides are common)

As the diagonals are congruent such that AC=BDand the diagonals of a parallelogram bisect such that BC=AD.

Therefore, by side-side-side postulate ΔABC≅ΔBAD.

Now, by CPCT theorem ∠ABC≅∠BAD.

Using the property of co-interior angles in a parallelogram.

∠ABC+∠BAD=1802∠ABC=180   ∴∠ABC≅∠BAD∠ABC=90

Therefore, the parallelogram is a rectangle.

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Most popular questions from this chapter

For the following figure, if WR¯⊥CE¯then name all segments congruent to WE¯.

Parallel rulers, used to draw parallel lines, are constructed so that EF=HGand HE=GF. Since there are hinges at points E, F, G and H, you can vary the distance between role="math" localid="1637730770232" HG↔and role="math" localid="1637730792914" EF↔. Explain why HG↔and EF↔are always parallel.

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