Primary 5 Properties of Triangles Study Guide
Primary 5 triangles in four short steps: naming a triangle, the 180° angle sum, drawing on a square grid, and drawing with a ruler and protractor. Each step has a figure to tap through, then worked examples and a five-question check.
Start here
What are the properties of a triangle?
Read the marks first: they say which sides and angles are equal.
A Primary 5 triangle is named by its angles (right-angled, acute-angled, obtuse-angled) or by its sides (equilateral, isosceles). Ticks and small squares on a figure state facts that the question may not write out. Together with the three angles adding up to 180°, those facts give the missing angles and guide an accurate drawing.
In this chapter, your child learns to:
- name a triangle from its angles or from the marks on its sides;
- use the properties of isosceles, equilateral and right-angled triangles;
- find an unknown angle from the angle sum of 180°;
- draw a right-angled or isosceles triangle on a square grid;
- draw a triangle from two sides and the angle between them.
ABC is a triangle with AB = AC. ∠BAC = 50°. Find ∠ABC.
- AB = AC(one tick on each: same mark, same length)
- ∠ABC = ∠ACB(the angles opposite the equal sides)
- ∠ABC = (180° − 50°) ÷ 2 = 65°(base angle of isosceles triangle ABC)
Step 1
Types of triangles and the marks that name them
The first three names come from an angle; the last two come from the sides. A small square marks a right angle. Ticks show which sides are the same length: same mark, same length, and a different mark means a different length. In an isosceles triangle, the two angles at the ends of the third side are its base angles, and they are equal. One triangle can carry two names, such as right-angled and isosceles.
Tap a name
Tap a name. Each triangle carries the marks that give it that name.
A triangle has angles of 79°, 55° and 46°. What kind of triangle is it?
Step 2
Angles in a triangle and the 180° angle sum
The three angles in a triangle add up to 180°. Minus the angles you know from 180° to find the last one. In an isosceles triangle, the two equal angles share what is left after the top angle, so your child writes (180° minus the top angle) ÷ 2 on a single line. The bracket beside each line says which property gave it.
Tap Next step
In triangle ABC, ∠ABC = 42° and ∠ACB = 63°. Find ∠BAC.
- ∠BAC = 180° − 42° − 63° = 75°(angle sum of triangle ABC)
PQR is a triangle and PQ and PR are the same length. ∠QPR = 100°. Find ∠PQR.
- ∠PQR = ∠PRQ(base angles of isosceles triangle PQR)
- ∠PQR = (180° − 100°) ÷ 2 = 40°(base angle of isosceles triangle PQR)
XYZ is a triangle with all three sides the same length. Find ∠XYZ.
- ∠XYZ = ∠YZX = ∠ZXY = 180° ÷ 3 = 60°(angles of equilateral triangle XYZ)
STU is a triangle with ST = SU. ∠STU = 68°. Find ∠TSU.
Step 3
Drawing a triangle on a square grid
On a grid, a side is a staircase: squares across, then squares up. Count how one end reaches the other along the ruled lines. For a right angle, turn that staircase a quarter turn about the corner, and the two counts swap over. The same two counts make the same length, so the turned staircase also gives an equal side. Then mark the right angle and the equal sides on the drawing.
Tap Next step
PQ is one side of triangle PQR. ∠PQR = 90° and QR = PQ. R is above PQ. Find R.
PQ is one side of triangle PQR. ∠PQR = 90° and QR = PQ. R is below PQ. Find R.
On a square grid, the pencil moves from A to B 4 squares right and 1 square up. BC leaves B at a right angle to AB and is as long as AB. C is above AB. From B, how does the pencil move?
Step 4
Drawing a triangle with a ruler and protractor
A construction is a direction and then a distance. Draw the side with a given length first. At its end, measure the given angle with a protractor and draw a line that way. Then measure the second length from the corner along that line, or swing an arc of that radius, to find the last vertex. Join it, and label every length and angle the question gave.
Tap Next step
Draw triangle DEF with DE = 7 cm, ∠DEF = 65° and EF = 5 cm.
To draw triangle GHJ, GH is drawn 8 cm long and a line leaves H at 40° to HG. HJ = 6 cm. Where is J?
Primary 5 properties of triangles questions, worked step by stepCover the working and try each one on paper first. Open the hint if you are stuck, then reveal one line per tap.
In triangle LMN, ∠LMN = 97°, ∠MNL = 41° and ∠NLM = 42°. What kind of triangle is LMN?
- 97° is more than 90°, so ∠LMN is an obtuse angle.
- 41° and 42° are less than 90°, so ∠MNL and ∠NLM are acute angles.
- A triangle with an obtuse angle is an obtuse-angled triangle.
In triangle RST, ∠RST = 62° and ∠STR = 49°. Find ∠SRT.
- ∠SRT + 62° + 49° = 180° (angle sum of triangle RST)
- ∠SRT = 180° − 62° − 49°
- = 69°
ABC is a triangle with AB = AC. ∠ABC = 53°. Find ∠BAC.
- ∠ACB = ∠ABC = 53° (base angles of isosceles triangle ABC)
- ∠BAC = 180° − 53° − 53° (angle sum of triangle ABC)
- = 74°
Triangle PQR has a right-angle square at Q, and PQ and QR each carry one tick. Name the triangle in two ways, then find ∠QPR.
- ∠PQR = 90°, so PQR is a right-angled triangle.
- PQ = QR, so PQR is also an isosceles triangle.
- ∠QPR = (180° − 90°) ÷ 2 (base angle of isosceles triangle PQR)
- = 45°
GH is one side of triangle GHK on a square grid. From G to H the pencil moves 4 squares right and then 3 squares up. ∠GHK is a right angle, HK = GH, and K lies below GH. From H, how does the pencil move to reach K?
- G to H = 4 right, 3 up
- ∠GHK = 90°, so HK leaves H square to GH
- a quarter turn about H swaps the counts: 3 and 4
- K is below GH, so from H: 3 right, then 4 down
Step 5
Check yourself
Five quick questions on naming, angle sums and drawing. Nothing is saved, and each reply points to the practice set that fits.
A triangle has angles of 90°, 34° and 56°. What kind of triangle is it?
All three sides of triangle DEF carry one tick. Find ∠DEF.
Two angles of a triangle are 48° and 67°. Find the third angle.
XYZ is a triangle with XY = XZ. ∠YXZ = 44°. Find ∠XYZ.
On a square grid, the pencil moves from S to T 2 squares right and 5 squares up. TU leaves T at a right angle to ST and is as long as ST. U is to the left of ST. From T, how does the pencil move?
Using this guide at home. Before any calculation, ask your child to point at each mark on the figure and say what it means: this square is a right angle, these two ticks are equal sides, so these two angles are equal. Those spoken facts usually choose the method. Then ask which property each line of working uses, and have it written in brackets.
For drawing, keep a sharp pencil, a ruler and a protractor nearby. On a grid, ask your child to count the staircase aloud before turning it. With a protractor, ask which side was drawn first, which way the next side goes, and how far along it the last corner sits. Finish by checking every given length and angle against the drawing.
More study guides
P5 Properties of Triangles lessons and practice
3 lesson videos and 21 questions across three subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →