Congruence of Triangles quiz

Two figures are congruent if they have the same:

Which is not a criterion for congruence of triangles?

If triangle ABC is congruent to triangle PQR, then side BC corresponds to:

RHS congruence applies only to:

In SAS congruence, the angle must be:

Two line segments are congruent if they have:

If triangle DEF is congruent to triangle XYZ and angle E = 75 degrees, then angle Y equals:

Two angles of 40 degrees each are:

In ASA congruence, the side must be:

Which of these are always congruent?

Give two examples of congruent objects in daily life. (2 marks)

If triangle PQR is congruent to triangle STU, write the corresponding angles. (2 marks)

Why is the order of letters important in a congruence statement? (2 marks)

Explain why two squares with equal sides are congruent. (2 marks)

What is the hypotenuse of a right triangle? (2 marks)

Is it possible for two triangles to have equal areas but not be congruent? Give an example. (2 marks)

In triangles ABC and DEF, AB = DE, BC = EF and AC = DF. Write the congruence and the criterion. (2 marks)

Why is SSA not a congruence criterion in general? (2 marks)

If triangle ABC is congruent to triangle ACB, what kind of triangle is ABC? (2 marks)

In two congruent triangles, one side measures 8 cm. What can you say about the corresponding side of the other triangle? (2 marks)

Triangle LMN is congruent to triangle XYZ. If LM = 5 cm, MN = 7 cm, angle L = 55 degrees and angle M = 65 degrees, find XY, YZ, angle Z and angle X. (3 marks)

In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Write the correct correspondence and the congruence statement. Name the criterion. (3 marks)

In right triangles ABC and DEF, angle B = angle E = 90 degrees, AC = DF = 10 cm and AB = DE = 6 cm. Find BC if EF = 8 cm. Name the criterion. (3 marks)

In triangle PQR, angle P = 50 degrees and angle Q = 70 degrees. In triangle XYZ, angle X = 50 degrees, angle Y = 70 degrees and PQ = XY = 6 cm. Find angle R and angle Z, and decide whether the triangles are congruent. (3 marks)

Two congruent triangles have perimeters equal. If the sides of one are 6 cm, 8 cm and 10 cm, find the perimeter of the other. Is the other triangle right-angled? Explain. (3 marks)

Read the passage and answer the questions. A carpenter is making identical triangular shelves. For each shelf, he cuts two sides of 30 cm and 40 cm with a right angle between them. (i) Which criterion ensures that all shelves are congruent? (ii) What will be the length of the third side? (iii) If he measured only the three angles, would the shelves be congruent? Explain. (5 marks)

Read the passage and answer the questions. In a kite-shaped design ABCD, AB = AD and CB = CD. The diagonal AC is drawn. (i) Name the two triangles formed by the diagonal. (ii) Are they congruent? By which criterion? (iii) Which angles at A are equal as a result? (5 marks)

Read the passage and answer the questions. Two ladders of equal length lean against a vertical pole from opposite sides, each reaching the same height on the pole. The pole makes a right angle with the level ground. (i) Which criterion shows the two triangles are congruent? (ii) What equal parts are given? (iii) What can you say about the distances of the ladders' feet from the pole? (5 marks)

Read the passage and answer the questions. In a bridge truss, a triangle ABC has AB = AC. A rod AD is fixed from A to the midpoint D of BC. (i) Name the two triangles formed. (ii) Show that they are congruent by naming the criterion. (iii) What can you conclude about angle ADB and angle ADC? (5 marks)

Read the passage and answer the questions. A student drew triangle PQR with PQ = 4 cm, QR = 5 cm and angle P = 50 degrees, and his friend drew triangle XYZ with XY = 4 cm, YZ = 5 cm and angle X = 50 degrees. Their triangles looked different. (i) Is the given angle between the two given sides? (ii) Why might the triangles not be congruent? (iii) What information would guarantee congruence? (5 marks)

State and illustrate with diagrams the four congruence criteria SSS, SAS, ASA and RHS. Give one example of each with measurements. (6 marks)

In the figure, AB and CD are equal and parallel, and AD and BC meet at O. Draw the figure and show that triangle AOB is congruent to triangle DOC. Hence show that O is the midpoint of AD and BC. (6 marks)

Draw triangle ABC in which AB = AC, and D is a point on BC such that BD = DC. Prove that triangle ABD is congruent to triangle ACD. Hence show that AD is perpendicular to BC and bisects angle A. (6 marks)

Explain with diagrams why AAA and SSA are not congruence criteria. Draw two triangles with angles 40, 60 and 80 degrees of different sizes, and two triangles with two sides and a non-included angle equal but not congruent. (6 marks)

Draw a square ABCD with diagonal AC. Show that triangle ABC is congruent to triangle CDA. Name the criterion and find the measure of angle BAC. (6 marks)