Question

Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.

A) reflect triangle 1 across the y-axis

B) reflect triangle 2 across the y-axis

C) rotate triangle 2 counter-clockwise 90° about the origin

D) reflect triangle 2 across the y axis and rotate 90° about the origin at

Answer 1

The correct option is C.

Explanation:

From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).

If a figure rotated counter-clockwise 90° about the origin, then

`(x,y)\rightarrow (-y,x)`

If we rotate triangle 2 counter-clockwise 90° about the origin, then[

`P(2,2)\rightarrow P'(-2,2)`

`Q(4,4)\rightarrow Q'(-4,4)`

`R(4,2)\rightarrow R'(-2,4)`

If we rotate triangle 2 counterclockwise, then we get the triangle 1.

Therefore the correct option is C.

Answer 2

The two triangles shown are congruent because triangle 1 has been formed from triangle 2 by rotating triangle 2 through and angle of 90°. Thus the correct answer will be:

C) rotate triangle 2 counter-clockwise 90° about the origin