Triangles - Properties and Congruence for Exam Success

Triangles - Properties and Congruence - Problems on Triangles - Case Studies

Q. If triangle PQR is similar to triangle STU and the length of PQ is 12 cm while ST is 16 cm, what is the ratio of PQ to ST?

Solution

The ratio of PQ to ST is 12:16, which simplifies to 3:4.

Correct Answer: A — 3:4

Q. If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:4?

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)² = 9/16.

Correct Answer: B — 9:16

Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what type of triangle is it?

Solution

Triangle ABC is isosceles because two angles are equal.

Correct Answer: B — Isosceles

Q. In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a right triangle?

Solution

Using the Pythagorean theorem, 7² + 5² = 49 + 25 = 74, and 10² = 100. Since 74 ≠ 100, triangle GHI is not a right triangle.

Correct Answer: A — Yes

Q. In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a right triangle?

Solution

Yes, because 9² + 12² = 81 + 144 = 225 = 15², satisfying the Pythagorean theorem.

Correct Answer: A — Yes

Q. What is the perimeter of triangle DEF if DE = 7 cm, EF = 5 cm, and DF = 6 cm?

Solution

The perimeter is the sum of all sides: 7 + 5 + 6 = 18 cm.

Correct Answer: A — 18 cm

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