Conditions for Similar Triangles

Are triangle ABC and triangle DEF similar?

• No

• Yes

Answer explanation

You can use AA~ (at least two angles congruent)

or

SAS~ (the sides 6:12 and 7:14 are proportional)

Are the triangles similar?

Hint: Find <A or <E first.

• Yes

• No

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA∼

• SAS∼

• SSS∼

• Not similar

Answer explanation

Both triangles have 71 and 30 degrees

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

Hint: Compare the shorter sides (6:12) and the longer sides (10:20)

• AA∼

• SAS∼

• SSS∼

• Not similar

Answer explanation

The angle between corresponding sides
is congruent

The sides are proportional
 $\frac{6}{12}=\frac{10}{20}$ 

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

Hint: Find the missing angle measures first. 

• AA∼

• SAS∼

• SSS∼

• Not similar

Answer explanation

Left triangle:
$180-32-78=70$
Both triangles have 70 and 78 agrees 

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

Hint: Compare the shortest sides, medium sides, and longest sides

• SSS∼

• SAS∼

• AA∼

• Not similar

Answer explanation

All 3 sides are proportional $\frac{10}{30}=\frac{15}{45}=\frac{20}{60}=0.\overline{33}$

$shortest\rightarrow medium\rightarrow longest$

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA∼

• SAS∼

• SSS∼

• Not similar

Answer explanation

$\frac{10}{20}\ne\frac{20}{30}$

The sides are NOT proportional

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SSS

• SAS

• Not similar

Answer explanation

All sides are proportional: $\frac{17}{37.4}=\frac{20}{44}=\frac{25}{55}=0.\overline{45}\$

$shortest\rightarrow medium\rightarrow longest$

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

Hint: Compare the shorter sides (48:60) and longer sides (56:70) 

• SSS

• AA

• SAS

• not similar

Answer explanation

Vertical Angles are are congruent

Sides are proportional
$\frac{48}{60}=\frac{56}{70}=0.8$

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SSS

• SAS

• Not similar

Answer explanation

$<F=45$
Both triangles have 45 and 29