Congruence and Similarity

Math ⇒ Geometry

Congruence and Similarity starts at 7 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Congruence and Similarity. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 7

If triangle ABC is congruent to triangle DEF, and AB = 7 cm, what is the length of DE?

If triangle ABC is congruent to triangle DEF, what can you say about the lengths of AB and DE?

If triangle ABC is congruent to triangle XYZ, and angle A = 50°, angle B = 60°, what is the measure of angle X?

If triangle ABC is similar to triangle DEF and AB = 5 cm, DE = 10 cm, and AC = 7 cm, what is the length of DF?

If triangle ABC is similar to triangle DEF and the scale factor is 2, what is the ratio of their areas?

If triangle PQR is similar to triangle XYZ and PQ = 4 cm, QR = 6 cm, and XY = 8 cm, what is the length of YZ?

A rectangle has length 8 cm and width 4 cm. Another rectangle is similar to it and has a length of 20 cm. What is its width?

A triangle has sides of length 6 cm, 8 cm, and 10 cm. Another triangle has sides of length 9 cm, 12 cm, and 15 cm. Are these triangles congruent or similar? Explain your answer.

Explain why all equilateral triangles are similar to each other, but not necessarily congruent.

Given two similar triangles, the lengths of the corresponding sides of the first triangle are 5 cm, 12 cm, and 13 cm. If the shortest side of the second triangle is 10 cm, what are the lengths of the other two sides?

If the ratio of the areas of two similar triangles is 9:16, what is the ratio of their corresponding sides?

A student claims that two rectangles with side lengths 3 cm by 6 cm and 6 cm by 12 cm are congruent. Is the student correct? Explain why or why not.

A triangle has angles measuring 40°, 60°, and 80°. Another triangle has angles measuring 40°, 60°, and 80°. Are these triangles necessarily congruent? Explain your answer.

A triangle has sides of length 7 cm, 24 cm, and 25 cm. Another triangle has sides of length 14 cm, 48 cm, and 50 cm. Are these triangles congruent, similar, or neither? Justify your answer.

If two polygons are similar and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?

Two triangles, △ABC and △DEF, have the following properties: AB = 6 cm, BC = 8 cm, AC = 10 cm, DE = 9 cm, EF = 12 cm, and DF = 15 cm. Prove whether the triangles are similar and state the similarity criterion used.