PQ is one side of triangle PQR on the grid below. Angle PQR is a right angle and QR is the same length as PQ. Draw and letter triangle PQR.
P to Q = 3 right, 1 up
Q to R = 1 left, 3 up
(a quarter turn, so 90° at Q)
QR = PQ
(the same 2 counts)
Join PR. Label 90° and QR = PQ.
Ans: R is 1 square left of Q and 3 squares up, with a right angle at Q and one tick on PQ and on QR
Example 1
Draw triangle ABC. AB and BC are both 6 centimetres. Angle ABC is one hundred and twenty five degrees.
Draw AB = 6 cm
Angle ABC = 125° at B
BC = 6 cm on that line
Join AC and tick the equal sides
Ans: triangle ABC with AB = BC = 6 cm, angle ABC = 125°, and one tick on AB and on BC
How to solve it
Draw the side the question gives a length for: AB, 6 centimetres long.
Fix the direction: draw a line out from B, opened until the angle it makes with BA is 125 degrees.
Fix the distance: every point on an arc 6 centimetres from B is the right distance. C is where the arc crosses the line.
Join A to C. One tick on AB and one on BC show the two equal sides.
Read the drawing back against the question: 6 centimetres, 6 centimetres and 125 degrees are all on the triangle.
The angle at B is the direction the second side leaves in. The arc is every point 6 centimetres from B, and C is the one of them on that line. A construction is a direction and then a distance.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its full working.
Question 1 of 6 · Basic · free to tryThe figure shows the side PQ of a triangle on a square grid. From P to Q the…The figure shows the side PQ of…
The figure shows the side PQ of a triangle on a square grid. From P to Q the pencil moves 4 squares right and then 2 squares up. The next side must leave Q at a right angle to PQ and be the same length as PQ. The third vertex is above Q. Starting at Q, how many squares does the pencil move to reach the third vertex?
the corner at Q is a right angle, so the next side leaves Q square to PQ
turn the staircase a quarter turn about Q: the 4 and the 2 swap over
from Q the pencil moves 2 left, then 4 up
Answer: 2 squares left and 4 squares up
For parents
How do you answer P5 drawing triangles questions accurately?
This page pairs the triangle properties in the Primary 5 Geometry strand with drawing: putting an isosceles or right-angled triangle on a square grid, and reading a ruler-and-protractor drawing.
What your child learns here
This page pairs the triangle properties in the Primary 5 Geometry strand with drawing: putting an isosceles or right-angled triangle on a square grid, and reading a ruler-and-protractor drawing. It builds on drawing angles and perpendicular lines from earlier years.
An isosceles triangle has two equal sides, and its top vertex lies directly above the middle of the base.
On a grid, a line at right angles to a slanted side is made by a quarter turn: the counts across and up swap over.
A side twice as long on a grid has both of its counts doubled.
With a ruler and protractor, one side is drawn first, the angle sets the direction, and compasses set the distance.
A finished drawing carries its marks and letters: ticks on equal sides, a square in a right angle, and a letter at each vertex.
Does the answer make sense?
On a grid, an equal side at right angles swaps the two square counts and turns one direction round: 5 right and 1 up becomes 1 left and 5 up, and twice as long doubles both. When your child draws two equal sides meeting above a level base, their vertex sits above its middle.
How to practise these questions
Basic questions train completing a triangle on a grid from one drawn side and stated lengths or angles, then lettering it. Intermediate questions add reading the radius of a finished construction and naming the marks a correct drawing still needs. The Challenge question asks your child to turn a side's grid steps into the steps of the side at right angles to it, running the other way. If the drawing goes off course, watch the solution film for that question, then try it again later from Revision.
Questions parents ask
What tools does my child need to draw triangles? A sharp pencil, a ruler and a protractor, and a pair of compasses for some drawings. Squared paper is used for questions set on a grid.
Is drawing triangles in the Primary 5 syllabus? The Primary 5 syllabus lists the properties of isosceles, equilateral and right-angled triangles. Drawing them on a grid applies those properties, together with drawing angles and perpendicular lines from earlier years.
Why must the drawing have ticks and letters? The marks show which sides are equal and which angle is a right angle, and the letters name each vertex. Without them, the drawing does not show what the question asked for.
