Discover Mathematics P4: Term 2, Unit 12, Lessons 11–14
GoalDecide if a triangle is possible and draw triangles on squared paper that follow given rules.
New words
possible · something that can exist or be drawnlegs of a right triangle · the two sides that make the right anglerule · a fact the shape must follow, such as “one right angle” or “two equal sides”
Explanation
To draw a triangle that fits the rules, first check that it is possible. A triangle can have only one right angle or one obtuse angle. An equilateral triangle is always acute. A triangle can be right and isosceles, or obtuse and isosceles, or right and scalene. But it cannot be right and equilateral. On squared paper, the lines of the grid make right angles, so we can draw a right triangle by drawing its two legs along the grid lines and joining their ends. For an isosceles triangle, draw the base along a grid line, find the middle of the base, go straight up from the middle, and join the top to both ends of the base. The two slanted sides are then equal. Mark equal sides with ticks and right angles with a small square.
Triangle
Possible?
right and isosceles
yes
obtuse and scalene
yes
right and equilateral
no
two right angles
no
Worked examples
Draw a right triangle with legs of 4 squares and 3 squares. Draw a line 4 squares long along the grid. From one end draw a line 3 squares straight up. Join the two free ends. The square at A shows the right angle. This triangle has three different side lengths, so it is a right scalene triangle.
Draw an isosceles triangle with a base of 6 squares. Draw the base. Find its middle, 3 squares from each end. Go 4 squares straight up and mark the top. Join the top to both ends. The two slanted sides are equal (the ticks) and all three angles are acute.
Is it possible? A triangle that is obtuse and isosceles is possible: a wide, flat triangle with two equal sides. A triangle with two right angles is impossible: the two sides on the base would both be perpendicular to it, so they would be parallel and would never meet at a top corner.
Class activity
Triangle designer. On squared paper draw four triangles: one right triangle, one isosceles triangle, one obtuse triangle and one that is both right and isosceles. Mark right angles with a small square and equal sides with ticks. Then write a rule card for each, such as: one right angle, two equal sides.
Practice
1
Can a triangle have two obtuse angles? Explain.
No. Two obtuse angles are each wider than a square corner, so the two sides would spread apart and never meet to close the triangle.
2
A right triangle has legs of 6 squares and 8 squares and a longest side of 10 squares. Is it scalene? Why?
Yes. The sides 6, 8 and 10 are all different.
3
Is a triangle with sides 5 cm, 5 cm and 5 cm and a right angle possible?
No. An equilateral triangle always has three acute angles.
4
Describe how to draw a right isosceles triangle with legs of 5 squares.
Draw 5 squares along a grid line, then 5 squares straight up from one end, and join the free ends. The two legs are equal.
5
Omar says an obtuse triangle can be isosceles. Is he right?
Yes. A wide, flat triangle with two equal sides has one obtuse angle.
