Question

2 - 114. which pairs of triangles below are congruent and/or similar? for each part, explain how you know using an appropriate triangle congruence or similarity condition. note: the diagrams are not necessarily drawn to scale. homework help

Explanation:

Step1: Check side - side - side (SSS) for part a

Compare side - length ratios. $\frac{6}{2}
eq\frac{12}{4}
eq\frac{15}{5}$, so not similar or congruent.

Step2: Check angle - angle (AA) for part b

In the first triangle, the third angle is $180-(20 + 112)=48^{\circ}$. In the second triangle, we have angles $48^{\circ}$ and $20^{\circ}$. Since two pairs of angles are equal, the triangles are similar by AA.

Step3: Check side - side - side (SSS) for part c

The sides of the first right - triangle are $5,12,13$ (a Pythagorean triple). The second right - triangle has sides $5,12,13$ in the same order. So, they are congruent by SSS.

Step4: Check angle - angle (AA) for part d

Two pairs of angles ($48^{\circ}$ and $62^{\circ}$) are equal in both triangles. Also, the included sides between the equal - angle pairs are equal. So, they are congruent by ASA (angle - side - angle) and similar.

Answer:

a. Neither congruent nor similar.
b. Similar (by AA).
c. Congruent (by SSS).
d. Congruent (by ASA) and similar.