Question

triangle properties , exterior angle property and angle sum property. ​

Answer 1

Explanation:

Triangle Exterior Angle Theorem

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

Remember that the two non-adjacent interior angles, which are opposite the exterior angle are sometimes referred to as remote interior angles.

For example, in triangle ABC above;

⇒ d = b + a

⇒ e = a + c

⇒ f = b + c

Properties of exterior angles

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The sum of exterior angle and interior angle is equal to 180 degrees.

⇒ c + d = 180°

⇒ a + f = 180°

⇒ b + e = 180°

All exterior angles of a triangle add up to 360°.

Proof:

⇒ d + e + f = b + a + a + c + b + c

⇒ d +e + f = 2a + 2b + 2c

= 2(a + b + c)

But, according to triangle angle sum theorem,

a + b + c = 180 degrees

Therefore, ⇒ d +e + f = 2(180°)

= 360°

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Answer 2

Answer:

Angle sum prop.triangle.prop.exter.angle.

Explanation:

Angle sum property=The sum of angles of a triangle=180 degrees.

Properties of a triangle:

A triangel cant have more than one rt.,obt. angle.

Sum of the acute angles is 90 degrees in a rt.angled triangle

Exterior angle=Sum of two interior angles=Exterior angle'

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