The Triangle and its Properties quiz

The sum of the interior angles of a triangle is:

A median joins a vertex to the:

Each angle of an equilateral triangle is:

An exterior angle of a triangle equals:

Which can be the sides of a triangle?

In a right triangle with legs 6 cm and 8 cm, the hypotenuse is:

The number of altitudes in a triangle is:

In an isosceles triangle, the angles opposite the equal sides are:

Which set is a Pythagorean triplet?

In a right-angled triangle, the longest side is the:

Two angles of a triangle are 80 degrees and 55 degrees. Find the third angle. (2 marks)

In an isosceles triangle, the vertex angle is 40 degrees. Find each base angle. (2 marks)

The exterior angle of a triangle is 120 degrees and the interior opposite angles are equal. Find them. (2 marks)

Is the triangle with sides 7 cm, 24 cm and 25 cm right-angled? Show. (2 marks)

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two lengths should the third side lie? (2 marks)

In an obtuse triangle, where can an altitude lie? Explain. (2 marks)

Find x if the angles of a triangle are x, 2x and 3x. (2 marks)

Where does the altitude of a right triangle from the vertex of the right angle meet? Where do the other two altitudes lie? (2 marks)

A right triangle has one acute angle of 35 degrees. Find the other acute angle. (2 marks)

Can the median and altitude of a triangle be the same? When? (2 marks)

Find the perimeter of a rectangle whose length is 40 cm and diagonal is 41 cm. (3 marks)

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter. (Diagonals of a rhombus bisect each other at right angles.) (3 marks)

In triangle ABC, angle A = 3x, angle B = 2x + 10 and the exterior angle at C is 110 degrees. Find x and all angles of the triangle. (3 marks)

Two poles of heights 6 m and 11 m stand on level ground 12 m apart. Find the distance between their tops. (3 marks)

Check whether triangles with these sides are right-angled: (i) 2.5 cm, 6.5 cm, 6 cm (ii) 2 cm, 2 cm, 5 cm (iii) 1.5 cm, 2 cm, 2.5 cm. (3 marks)

Read the passage and answer the questions. A park is in the shape of a right triangle. Two paths along the legs are 80 m and 60 m long. Children take a shortcut along the hypotenuse. (i) Find the length of the shortcut. (ii) How much distance do they save compared to walking along both legs? (iii) Name the property used. (5 marks)

Read the passage and answer the questions. A roof truss is an isosceles triangle with the angle at the top equal to 100 degrees. (i) Find each base angle. (ii) What type of triangle is it by angles? (iii) Find the exterior angle at one base vertex. (5 marks)

Read the passage and answer the questions. Rina walks 24 m due east and then 7 m due north from her house. (i) Draw a rough path diagram in words. (ii) Find how far she is from her house in a straight line. (iii) Which property did you use? (5 marks)

Read the passage and answer the questions. Three villages A, B and C are joined by straight roads. AB = 8 km and BC = 5 km. (i) Can AC be 15 km? Why? (ii) Between what values must AC lie? (iii) If AC is a whole number of km, what is its largest possible value? (5 marks)

Read the passage and answer the questions. A kite string makes a triangle with the ground. The string is 50 m long and the kite is directly above a point 30 m from the person. (i) Find the height of the kite. (ii) What type of triangle is formed? (iii) Name the hypotenuse. (5 marks)

Describe an activity to verify the angle sum property of a triangle by cutting and arranging the three corners. Draw the figure and explain the result. (6 marks)

Draw a triangle ABC with BC extended to D. Prove using the angle sum property that angle ACD = angle A + angle B. Verify with angle A = 50 degrees and angle B = 60 degrees. (6 marks)

Draw an acute, a right and an obtuse triangle. In each, draw all three altitudes and describe where they lie. (6 marks)

Explain the property that the sum of any two sides of a triangle is greater than the third side using an activity with sticks or a diagram of three towns. Check the sides 4 cm, 5 cm, 10 cm and 6 cm, 7 cm, 10 cm. (6 marks)

Draw a right triangle PQR with angle Q = 90 degrees, PQ = 9 cm and QR = 12 cm. Find PR. Draw the median from P to QR and the altitude from Q to PR, and find the area of the triangle. (6 marks)