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 12

Describe a real-world application where triangle similarity is used.

Describe the SSS (Side-Side-Side) similarity criterion for triangles.

Explain the difference between congruence and similarity in geometric figures.

Explain why the SSA condition does not guarantee triangle congruence.

Given △PQR ~ △XYZ, if PQ = 6 cm, QR = 8 cm, PR = 10 cm, and XY = 9 cm, find the length of YZ.

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

Given: In △ABC and △DEF, AB = DE, BC = EF, and ∠B = ∠E. Are the triangles congruent?

If two equilateral triangles have sides of 6 cm and 10 cm respectively, are they congruent?

If △ABC ≅ △DEF, which of the following statements is always true? (1) AB = DE (2) ∠A = ∠E (3) BC = EF (4) All of the above

Which of the following is a correct statement about congruent triangles? (1) They have equal corresponding sides and angles. (2) They have equal areas but not necessarily equal sides. (3) They have equal perimeters but not necessarily equal angles. (4) They have equal corresponding angles but not necessarily equal sides.

Which of the following is NOT a criterion for triangle congruence? (1) SSS (2) SAS (3) ASA (4) SSA

Which of the following is NOT a property of congruent figures? (1) Same shape (2) Same size (3) Same orientation (4) Corresponding sides are equal

Fill in the blank: If two triangles are congruent, then their corresponding ________ are equal.

Fill in the blank: If two triangles have their corresponding sides in the ratio 1:2, then the ratio of their areas is ________.

Fill in the blank: The ________ criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Fill in the blank: The AAA criterion is sufficient to prove that two triangles are ________.

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

Given: In △ABC and △DEF, AB = DE, BC = EF, and ∠B = ∠E. Are the triangles congruent?

If two equilateral triangles have sides of 6 cm and 10 cm respectively, are they congruent?

If two right triangles have their hypotenuses and one leg equal, are they congruent?