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Primary 5 Properties of Triangles study guide: the whole chapter, step by step
About this subtopic
This mixed practice stop brings together 3 topics from Primary 5 Properties of Triangles: Five kinds of triangle, Inside one triangle, Drawing a triangle. Nothing on the question says which topic it comes from, so choosing the method is part of the skill.
Practice questions with worked solutions
Question 1 is free to try. The other 2 open in the free trial, each with its full working.
Print this subtopic · included with a plan
2 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.
Start the 7-day free trialQuestion 1 of 3 · Intermediate · free to tryThe figure shows triangle PQR. PQ = QR and angle PQR = 90°. S is a point on…The figure shows triangle PQR…
The figure shows triangle PQR. PQ = QR and angle PQR = 90°. S is a point on QR and PS is drawn. Angle SPR = 28°. The figure is not drawn to scale. Find angle PSR.
Show the working and the answer
Working
- PQ = QR (one tick on PQ and one on QR)
- ∠QPR = ∠QRP (the two angles opposite the equal sides PQ and QR)
- ∠PQR = 90° (the right-angle square at Q)
- ∠QRP = (180° − 90°) ÷ 2 = 45° (base angle of isosceles triangle PQR)
- ∠PSR = 180° − 45° − 28° = 107° (angle sum of triangle PSR)
Answer: 107°
For parents
How should my child use the properties in P5 triangles mixed practice?
Each question here links the kind of triangle with its angles, in one direction or the other.
What your child learns here
Each question here links the kind of triangle with its angles, in one direction or the other. Equal sides marked on the figure give equal angles; the angle sum gives the third angle, which then names the triangle as acute-angled, right-angled or obtuse-angled; and two kinds of triangle joined along a side share a corner. These are the Primary 5 Triangle outcomes: the properties of isosceles, equilateral and right-angled triangles, the angle sum, and finding unknown angles.
- The angles of every triangle add up to 180°.
- In an isosceles triangle, the two angles that face the equal sides match each other.
- All three angles of an equilateral triangle are 60°, because its three sides are equal.
- A triangle is named by its largest angle: less than 90° is acute-angled, exactly 90° is right-angled, more than 90° is obtuse-angled.
- When two triangles share a corner, the angle there is the sum of one angle from each triangle.
Does the answer make sense?
In the question that names triangle DEF, the third angle is 180° minus 58° minus 33°, which is 89°. That is just under 90°, so every angle is acute and DEF is acute-angled. Adding 58°, 33° and 89° back to 180° confirms the third angle before the name is given.
How to practise these questions
All three questions are Intermediate. One gives a right-angled isosceles triangle with a line drawn from one corner, so the equal sides give 45° angles before the angle sum finds the angle asked for. One gives two angles of a triangle and asks what kind of triangle it is, which needs the third angle first. One joins an equilateral triangle and an isosceles triangle along a shared side and asks for one angle inside the second triangle and one across both. Ask your child to say which sides are equal before finding any angle.
Questions parents ask
How is an equilateral triangle different from an isosceles one? An equilateral triangle has all three sides equal and every angle 60°. An isosceles triangle has two equal sides, so only its two base angles must match.
Why find the third angle before naming the triangle? A triangle is named by its largest angle, and the largest may be the one not given. Two acute angles do not make a triangle acute-angled on their own.
What do the tick marks on the sides mean? Sides with the same tick marks are equal. They tell your child which angles are equal, even when the figure is not drawn to scale.