Example 1
Show that each angle of a rectangle is a right angle.
Given: A rectangle ABCD
To prove: ∠ A = ∠ B = ∠ C = ∠ D = 90°
Proof:
We know that
Rectangle is a parallelogram where one angle is 90°.
Hence, lets assume
∠ A=90°
Now,
AD ∥ BC
& AB is a transversal
So, ∠ A + ∠ B = 180°
∠ B + 90° = 180°
∠ B = 180° – 90°
∠ B = 90°
Now, we know that
opposite angles of parallelogram are equal
∴ ∠ C = ∠ A and ∠ D = ∠ B
∴ ∠ C = 90° and ∠ D = 90°.
So , each of the angles of a rectangle is a right angle.
Hence proved

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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