Question

Triangle X has m2A = 30°, mZB = 90°, and m2C = 60° with side lengths of AB = 3, BC = 4, AC = 5.
Triangle Y has m2A = 30°, mZB = 90°, and mZC = 60' with side lengths of AB = 9, BC = 12, AC = 15.
Which statement best describes the relationship between these two triangles?
O They are similar triangles.
O They are similar and congruent triangles.
O They are congruent triangles.
O They are congruent but not similar triangles.

Answer 1

Answer:

O They are similar triangles.

Step-by-step explanation:

Given

Triangle X

$\angle A = 30$°, $\angle B = 90$°,  $\angle C = 60$°

$AB = 3,\ BC = 4,\ AC = 5.$

Triangle Y

$\angle A = 30$°, $\angle B = 90$°,  $\angle C = 60$°

$AB = 9,\ BC = 12,\ AC = 15.$

Required

The relationship between X and Y

From the given parameters, the corresponding angles of both triangles are equal i.e.

A = A, B = B and C = C

However, the side lengths are not equal.

The side lengths of Y is 3 multiplied by the side lengths of X.

This is shown below:

Triangle X

$AB = 3,\ BC = 4,\ AC = 5.$

Multiply by 2 to get Triangle Y

$AB= 3 * 3 = 9$

$BC= 4 * 3 = 12$

$AC = 5 * 3 = 15$

Since side lengths are not equal, but they have a common ratio of 3, then the triangles are similar.