Triangles quiz

Which of these is not a congruence rule?

In triangle ABC, AB = AC and angle B = 50 degrees. Angle C is:

Each angle of an equilateral triangle is:

The RHS congruence rule applies to:

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

Two triangles with all three angles equal are:

In an isosceles triangle, if the vertex angle is 80 degrees, each base angle is:

The congruence rule taken as an axiom is:

CPCT stands for:

If two sides and the included angle of one triangle are equal to those of another, the triangles are congruent by:

Why is SSA not a valid congruence rule? Give a reason. (2 marks)

In triangle PQR, angle P = angle Q. What can you say about the sides? (2 marks)

Show that the angles of an equilateral triangle are 60 degrees each. (2 marks)

Triangle DEF is congruent to triangle LMN. Write all the pairs of corresponding parts. (2 marks)

Two triangles have two angles and a non-included side equal. Are they congruent? Name the rule. (2 marks)

In triangle ABC, AB = AC = 6 cm and angle A = 60 degrees. Find BC. (2 marks)

Show that the diagonal of a square divides it into two congruent triangles. (2 marks)

In a right triangle, the hypotenuse and one side are equal to those of another right triangle. Are they congruent? Name the rule. (2 marks)

If the base angles of a triangle are 65 degrees each, find the vertex angle. (2 marks)

Give one example from daily life of congruent objects. (2 marks)

In an isosceles triangle, each base angle is twice the vertex angle. Find all the angles. (3 marks)

In triangle ABC, AB = AC and angle A = (x + 20) degrees and angle B = 2x degrees. Find x and all the angles. (3 marks)

Triangle ABC is congruent to triangle DEF. If AB = 4 cm, BC = 6 cm, AC = 5 cm, find the perimeter of triangle DEF. If angle A = 75 degrees and angle B = 55 degrees, find angle F. (3 marks)

In an isosceles right triangle, find each of the acute angles. If each equal side is 5 cm, find the hypotenuse in terms of the square root of 2. (3 marks)

ABC is an isosceles triangle with AB = AC. The bisectors of angles B and C meet at O. If angle A = 40 degrees, find angle OBC, angle OCB and angle BOC. (3 marks)

Read the passage and answer the questions. A roof truss is in the shape of an isosceles triangle ABC with AB = AC = 5 m and base BC = 8 m. A vertical support AD is placed from A to the mid-point D of BC. (i) Prove that triangle ABD is congruent to triangle ACD. (ii) Show that AD is perpendicular to BC. (iii) Find the length of AD. (5 marks)

Read the passage and answer the questions. Two friends stand at points P and Q on opposite banks of a river. To find the width PQ, Riya walks along her bank from P to a point R, puts a stick at the mid-point M of PR, then walks perpendicular to the bank from R to S such that Q, M and S are in a line. (i) Which two triangles are congruent? (ii) Name the congruence rule used. (iii) Why does RS equal the width of the river? (5 marks)

Read the passage and answer the questions. A kite ABCD has AB = AD and CB = CD, with diagonal AC. (i) Prove that triangle ABC is congruent to triangle ADC. (ii) Show that AC bisects angle A. (iii) Name the congruence rule used. (5 marks)

Read the passage and answer the questions. A ladder of length 5 m leans against a wall. Another ladder of the same length leans against the opposite wall. Both reach the same height of 4 m. (i) Prove the two triangles formed are congruent. (ii) Name the congruence rule. (iii) How far is the foot of each ladder from its wall? (5 marks)

Read the passage and answer the questions. A flag is shaped as triangle ABC with AB = AC. Points D and E are on BC such that BD = CE. (i) Prove that triangle ABD is congruent to triangle ACE. (ii) Show that AD = AE. (iii) What can you say about triangle ADE? (5 marks)

Prove the ASA congruence rule using the SAS axiom. Draw neat figures. (6 marks)

Prove that if two sides of a triangle are equal, the angles opposite them are equal. Use it to find the angles of an isosceles triangle whose vertex angle is 100 degrees. (6 marks)

AD is an altitude of an isosceles triangle ABC with AB = AC. Prove that AD bisects BC and angle A. Draw a neat figure. (6 marks)

Prove that the medians to the equal sides of an isosceles triangle are equal. Draw a figure and state each step. (6 marks)

In a right triangle ABC, right-angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to D so that DM = CM, and D is joined to B. Prove that triangle AMC is congruent to triangle BMD, that angle DBC is a right angle and that CM is half of AB. (6 marks)