Question

#1) What is the measure of ∠TVU, and why?

A) y, because ΔRST is similar to ΔVUT
B) y over 2, because ΔRST is congruent to ΔVUT
C) y + 55 degrees, because ΔRST is similar to ΔTUV
D) 125 degrees − y, because ΔRST is congruent to ΔTUV


#2) Which relationship is always true for the angles x, y, and z of triangle ABC?
A) x + z = y
B) y + z = x
C) x + y + z = 180 degrees
D) x + y + z = 90 degrees

#3) )A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p

In which step did the student first make a mistake and how can it be corrected?

A) Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
B) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
C) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles
D) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)

Answer 1

a

Explanation:

Answer 2

1) Answer: A

because trangles RST is similar to VUT as:

<RST=<VUT=55 (Angle)

<RTS=<VTU=90 (it seems right angled) Angle

So by AA similarity...(two angles similarity is enough)

2) Answer:B

y+z=x because exterior angle of a triangle (which is x) must be equal to sum of non-adjacent (y and z) interior angles.

3) Answer: A should be right choice. Step 1 is wrong here which is,

m<m + m<n + m<p=180 (wrong)

It should be:

m<m + m<n + m<0=180 (right)