Back to Exercise: Triangle similarity criteria (AA, SAS, SSS) and proportional sides

Triangle Similarity (AA, SAS, SSS) and Proportional Sides

Grade 10·22 problems·~30 min·ACT Math·topic·act-geo-tri-similar

Printable layout

Recall / Warm-Up

What is the sum of the interior angles of any triangle?

90°

180°

270°

360°

In a triangle, the angles measure 45° and 65°. What is the measure of the third angle?

60°

70°

80°

110°

Solve for $x$ :
$\frac{3}{5} = \frac{x}{20}$

Fluency Practice

In $\triangle ABC$ , $\angle A = 50\degree$ and $\angle B = 70\degree$ . In $\triangle DEF$ , $\angle D = 50\degree$ and $\angle E = 70\degree$ . Are the triangles similar? If so, by which criterion?

Yes, by AA

Yes, by SSS

Yes, by SAS

No, there is not enough information

Triangle 1 has sides 4, 6, and 8. Triangle 2 has sides 6, 9, and 12. Are the triangles similar?

Yes, by SSS — all three side ratios equal 2:3

Yes, by SSS — all three side ratios equal 3:4

No — only two side ratios are equal

No — the triangles have different perimeters

$\triangle ABC \sim \triangle DEF$ . If $AB = 10$ , $DE = 6$ , and $BC = 15$ , find $EF$ .

$\triangle PQR \sim \triangle XYZ$ . If $PQ = 8$ , $QR = 12$ , $XY = 6$ , find $YZ$ .

In $\triangle ABC$ , $AB = 12$ , $AC = 18$ , and $\angle A = 55\degree$ . In $\triangle DEF$ , $DE = 8$ , $DF = 12$ , and $\angle D = 55\degree$ . Are the triangles similar?

Yes, by SAS — two pairs of sides are proportional and the included angles are equal

Yes, by AA — the included angles are equal

No — the side ratios are not equal

No — SAS only works for congruence, not similarity

$\triangle ABC \sim \triangle DEF$ with scale factor $k = 3$ (where $k = AB/DE$ ). If $AC = 21$ , find $DF$ .

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

Create free account