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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°

 

Please Help Me With These Last Three Questions!!!

 May 7, 2018
 #1
avatar+7350 
+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  =  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  =  \(\frac{n\sqrt2}{2}\)

.
 May 7, 2018
 #2
avatar+7350 
+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°

 May 7, 2018
edited by hectictar  May 7, 2018

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