ACT — mathMedium1 min read

Similar and Congruent Triangles

Apply similarity and congruence criteria for triangles on the ACT. Use proportions to find missing measurements.

Tutor AI Team2026-02-25T02:03:17.402Z

Similar and congruent triangle questions are common on the ACT. They test proportional reasoning and the ability to identify matching parts.

Similar Triangles

Same shape, different size. Corresponding angles equal, sides proportional.

AA criterion: Two equal angles → similar.

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = k$ (scale factor)

Area ratio = $k^2$ . Volume ratio = $k^3$ .

Same shape AND size. Criteria: SSS, SAS, ASA, AAS, HL.

Problem

Triangles with sides 6, 8, 10 and 9, 12, ?. Scale factor = $\frac{9}{6} = 1.5$ . Missing side = $10 \times 1.5 = 15$ .

Solution

Problem

A 6-ft person casts a 4-ft shadow. A tree casts a 20-ft shadow. Tree height: $\frac{h}{20} = \frac{6}{4}$ → $h = 30$ ft.

Solution

1. Similar triangles: small has sides 5, 7, 9. Large has shortest side 15. Find the other sides.
1. Scale factor 2:5. Small area = 20. Large area = ?

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#act#math#geometry#similar-triangles#congruence

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