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 11

Describe a real-world application where similarity of triangles is used.

Describe the difference between congruence and similarity in geometric figures.

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

Explain why two rectangles with the same side ratios are similar but not necessarily congruent.

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

Given two similar rectangles, the length and width of the first are 8 cm and 5 cm, and the length of the second is 16 cm. What is the width of the second rectangle?

Given two similar triangles, △ABC and △DEF, with AB/DE = 2/3, what is the ratio of their areas?

Given two triangles, △ABC and △DEF, with AB = 5 cm, BC = 7 cm, CA = 8 cm, DE = 10 cm, EF = 14 cm, and FD = 16 cm, are the triangles similar?

If △ABC ≅ △DEF, which of the following statements is true? (1) AB = DE (2) ∠A = ∠F (3) BC = EF (4) AC = DF

Which of the following is a correct statement about congruent triangles? (1) All corresponding sides are equal. (2) All corresponding angles are equal. (3) Both (1) and (2) (4) None of the above

Which of the following is a similarity transformation? (1) Translation (2) Dilation (3) Reflection (4) Rotation

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

Fill in the blank: If two polygons are similar, then their corresponding angles are ________ and their corresponding sides are ________.

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

Fill in the blank: The ________ criterion states that if three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar.

Fill in the blank: The AA similarity criterion for triangles requires that at least ________ pairs of corresponding angles are equal.

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

If two triangles have sides in the ratio 3:4:5 and 6:8:10, are they similar?

True or False: All congruent figures are also similar.

True or False: If two polygons are similar, then their corresponding diagonals are also proportional.