True or False. A right triangle with two congruent legs is always a 45-45-90 triangle.

Mathematics

2 answers:

leva [86]2 years ago

8 0

Answer:

true

Step-by-step explanation:

Jet001 [13]2 years ago

5 0

Answer:

The given statement is true.

Step-by-step explanation:

Given a statement

A right triangle with two congruent legs is always a 45-45-90 triangle.

we have to check the above statement either it is true or false.

Given a right triangle,

⇒ one of the angle of triangle is right angle i.e of 90°

Now, given two legs of right triangle are equal i.e the triangle is isosceles i.e two angle other than 90° are equal let these are x

By angle sum property of triangle, sum of all angles of triangle is 180°

⇒ 90°+x+x=180°

⇒ 2x=180°-90°=90°

⇒ x=45°

Hence, other two angles are of 45°

⇒ A right triangle with two congruent legs is always a 45-45-90 triangle.

∴ The statement is true.

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