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Olympiad (Class 7) Triangles and congruence of triangles — practice questions — page 2

Explore 57 free Triangles and congruence of triangles questions in Olympiad (Class 7) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Triangles and congruence of triangles questions and exercises with answers

Showing questions 31–57 of 57.

Why are triangular frames used to make rigid structures?Read the answer and worked solution →Rods of fixed length are hinged at their ends. Which frame keeps its shape?Read the answer and worked solution →A line from a vertex to the midpoint of the opposite side is called what?Read the answer and worked solution →The three medians of a triangle meet at a point called what?Read the answer and worked solution →The three angle bisectors meet at the centre of a circle that does what?Read the answer and worked solution →A median is 18 cm long. How far is the centroid from the vertex along it?Read the answer and worked solution →The circumcentre lies on a side of a triangle. What is the angle opposite that side?Read the answer and worked solution →The legs of a right triangle are 6 cm and 8 cm. What is the hypotenuse?Read the answer and worked solution →A right triangle has hypotenuse 17 cm and one leg 8 cm. Find the other leg.Read the answer and worked solution →Which of these is a Pythagorean triple?Read the answer and worked solution →A triangle has sides 7 cm, 8 cm and 10 cm. Is it right-angled?Read the answer and worked solution →The square on a hypotenuse has area 169 cm² and the square on one leg has 25 cm². Find the other leg.Read the answer and worked solution →A 25 m ladder leans on a wall with its foot 7 m from the wall. How high does it reach?Read the answer and worked solution →A rectangle measures 9 cm by 12 cm. How long is its diagonal?Read the answer and worked solution →An isosceles triangle has equal sides 13 cm and base 10 cm. How long is its altitude to the base?Read the answer and worked solution →Asha walks 20 m north, then 21 m east. How far is she from her start in a straight line?Read the answer and worked solution →Why can a triangle never have two obtuse angles?Read the answer and worked solution →How many different-sized triangles can have angles 40°, 60° and 80°?Read the answer and worked solution →Three points lie on one straight line. How many proper triangles do they determine?Read the answer and worked solution →An exterior angle of a triangle is 100° and the two far interior angles are equal. Find each.Read the answer and worked solution →Interior angles are in the ratio 1:2:3. What is the exterior angle at the smallest angle?Read the answer and worked solution →In triangle ABC, AB = AC and D is the midpoint of BC. Triangles ABD and ACD are congruent by which rule?Read the answer and worked solution →One triangle has sides 5, 7, 9 cm. Another has sides 9, 5, 7 cm. Are they congruent?Read the answer and worked solution →Two triangles each have sides 6 cm and 8 cm and a 30° angle not between them. Are they congruent?Read the answer and worked solution →Two triangles each have angles 40° and 60°, and the side opposite 40° is 8 cm in both. Which rule applies?Read the answer and worked solution →The yield road sign has the shape of which triangle?Read the answer and worked solution →In which ancient work were the names for classifying triangles defined?Read the answer and worked solution →

Worked practice questions

Why are triangular frames used to make rigid structures?

  1. Three side lengths fix the shape
  2. The angles can be adjusted freely
  3. A triangle has the most corners
  4. A triangle is always the lightest
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Correct answer: A. Three side lengths fix the shape

Once the three side lengths are fixed the angles cannot change, so the frame cannot be squashed.

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Rods of fixed length are hinged at their ends. Which frame keeps its shape?

  1. Square
  2. Triangle
  3. Rectangle
  4. Rhombus
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Correct answer: B. Triangle

A square, rectangle or rhombus can lean over into a slanted shape, but the three fixed sides of a triangle leave no freedom to change.

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A line from a vertex to the midpoint of the opposite side is called what?

  1. Altitude line
  2. Angle bisector
  3. Median line
  4. Midpoint line
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Correct answer: C. Median line

A segment from a vertex to the midpoint of the facing side is a median.

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