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 10

A triangle has sides 8 cm, 15 cm, and 17 cm. Another triangle has sides 16 cm, 30 cm, and 34 cm. Are these triangles congruent or similar?

Describe the difference between congruence and similarity in geometric figures.

Explain why all equilateral triangles are similar to each other.

Explain why the AAA criterion is not sufficient for triangle congruence.

Given two similar triangles, △PQR and △XYZ, with PQ = 6 cm, QR = 8 cm, and XY = 9 cm. What is the length of YZ?

Given two similar triangles, if the length of a side in the first triangle is 5 cm and the corresponding side in the second triangle is 15 cm, what is the scale factor from the first to the second triangle?

Given two similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?

If △ABC ≅ △DEF and AB = 7 cm, what is the length of DE?

If two polygons are similar, what can you say about the ratio of their corresponding sides and the ratio of their areas?

State the SAS criterion for triangle congruence.

State the SSS similarity criterion for triangles.

A right triangle has legs of length 9 cm and 12 cm. A second right triangle has legs of length 15 cm and 20 cm. Are these triangles congruent, similar, or neither? Justify your answer.

Explain why the SSA (Side-Side-Angle) condition does not guarantee triangle congruence or similarity in all cases.

Given that △ABC ~ △DEF, and AB = 3 cm, BC = 4 cm, AC = 5 cm, and DE = 6 cm, find the lengths of EF and DF.

Given two triangles, △ABC and △DEF, where AB = 5 cm, AC = 7 cm, DE = 10 cm, DF = 14 cm, and ∠A = ∠D. Prove whether the triangles are similar and state the similarity criterion used.

If two triangles are similar and the ratio of their corresponding sides is 4:7, what is the ratio of their areas?

Two similar triangles have perimeters of 24 cm and 36 cm. If the shortest side of the smaller triangle is 6 cm, what is the length of the corresponding side in the larger triangle?