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# 3 Geometry Questions That I Really Need Help With!!! {5/7/18}

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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°

May 7, 2018

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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  =  n2

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

(BC)2 + (BC)2  =  n2

Combine like terms.

2(BC)2  =  n2

Divide both sides of the equation by  2 .

(BC)2  =  n2 / 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  =  $$\frac{n\sqrt2}{2}$$

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May 7, 2018
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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°

May 7, 2018
edited by hectictar  May 7, 2018