32)

The measure of side BC=

A: \(n\)

B: \(n\sqrt{2}\)

C: \(\sqrt{2}\)

D: \(\frac{n\sqrt{2}}{2}\)

40) You are given two triangles and the information that the three pairs of corresponding angles are congruent. What other information would guarantee that the triangles are congruent?

A: The triangles are right.

B: All corresponding sides are proportional.

C: One pair of corresponding sides is proportional.

D: One pair of corresponding sides has the same measure.

43)

If minor arc AC = 96°, what is the measure of ∠ABC?

A: 53°

B: 64°

C: 72°

D: 84°

Please Help Me With These Last Three Questions!!!

KennedyPape
May 7, 2018

#1**+2 **

**32)**

Since the sum of the angle measures in every triangle is 180°,

and we know that two of the angles are 90° and 45°.....

the measure of the third angle = m∠A = 180° - 90° - 45° = 45°

Since m∠A = m∠C , triangle ABC is isosceles and AB = BC

By the Pythagorean Theorem...

(AB)^{2} + (BC)^{2} = n^{2}

We can replace AB with BC since they are the same length.

(BC)^{2} + (BC)^{2} = n^{2}

Combine like terms.

2(BC)^{2} = n^{2}

Divide both sides of the equation by 2 .

(BC)^{2} = n^{2} / 2

Take the positive square root of both sides.

BC = \(\sqrt{\frac{n^2}{2}}\)

Simplify.

BC = \(\frac{\sqrt{n^2}}{\sqrt2}\)

BC = \(\frac{n}{\sqrt2}\)

Rationalize denominator.

BC = \(\frac{n\sqrt2}{2}\)

hectictar
May 7, 2018

#2**+2 **

**40)**

You are given two triangles and the information that the three pairs of corresponding angles are congruent. What other information would guarantee that the triangles are congruent?

D: One pair of corresponding sides has the same measure.

**43)**

If minor arc AC = 96°, what is the measure of ∠ABC?

Here's how I have to think of these....

Draw the angle that forms minor arc AC...its measure is 96° .

Even though it wasn't specifically stated in the question, I assume that lines AB and BC are tangent to the circle. That means line AB and line BC each forms a right angle with the line drawn from the center of the circle to point A and point C respectively.

The sum of the angle measures in every quadrilateral is 360° . So....

m∠ABC = 360° - 90° - 90° - 96° = 180° - 96° = 84°

hectictar
May 7, 2018