Pack B — Fluency

Mathematics

Year 8 · 8.14 Triangles

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
A triangle has angles 42° and 73°. Find the third angle.
2.
An isosceles triangle has apex angle 100°. Find each base angle.
3.
In triangle ABC, $\widehat{ABC} = 50°$ and $\widehat{BCA} = 70°$ . Find $\widehat{BAC}$ .
4.
Classify the triangle with sides 3, 4, 5 cm.
5.
Can a triangle have sides 3, 4, 8 cm? Justify using the triangle inequality.
6.
State the uniqueness conditions for triangles (SSS, SAS, ASA, RHS).
7.
In an equilateral triangle, what is each interior angle?
8.
A triangle has angles 90°, 35°, $x$ . Find $x$ .
9.
Classify by sides: a triangle has two sides of equal length. State the name.
10.
Classify by angles: a triangle has one angle of 120°. State the type.

SilverQuestions 11–20

11.
A triangle has angles $(2x + 10)°$ , $(3x - 5)°$ and $90°$ . Find $x$ .
12.
In triangle ABC, sides $a, b, c$ correspond to vertices $A, B, C$ . If $a = 6$ , $b = 8$ , $c = 10$ , identify which is the longest, the smallest, and find the right angle (if any).
13.
A triangle has sides 7, 9, $x$ cm. The triangle inequality requires what range for $x$ ?
14.
A triangle is isosceles with base 8 cm and equal sides 6 cm each. Calculate (a) the perimeter, (b) the height from the apex to the base, (c) the area.
15.
Two triangles have sides 3, 4, 5 and 5, 12, 13. Are they congruent? Similar?
16.
Two triangles have sides 6, 8, 10 and 12, 16, 20. Are they similar?
17.
The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. If interior angles are 40° and 60°, find the exterior angle at the third vertex.
18.
A right-angled triangle has legs 5 and 12. Find the hypotenuse.
19.
A right-angled triangle has hypotenuse 25 and one leg 7. Find the other leg.
20.
A triangle has sides labelled $a$ , $b$ , $c$ . State which side is opposite vertex $A$ and explain the naming convention.

GoldQuestions 21–30

21.
In a figure with two parallel lines and a transversal, one angle is $(3x - 10)°$ and the corresponding angle on the other line is $(2x + 35)°$ . Find $x$ .
22.
Triangle ABC has $A = (0, 0)$ , $B = (4, 0)$ , $C = (4, 3)$ . (a) Find the perimeter. (b) Classify by sides and angles.
23.
A triangle has angles $(2x)°, (3x + 10)°$ and $(x - 10)°$ . Find $x$ and the three angles.
24.
An isosceles triangle has perimeter 30 cm and base 8 cm. Find the equal sides.
25.
A triangle has angles $(x + 20)°$ , $(2x - 10)°$ , $(3x)°$ . (a) Find $x$ . (b) Classify the triangle.
26.
A 3D Pythagoras-flavoured problem: a rectangular room is 4 m × 3 m × 2 m. Find the longest diagonal.
27.
Two triangles with the same sides (SSS) are always congruent. True or false? Justify.
28.
A 2D figure on a coordinate plane has vertices $A(0,0), B(6,0), C(3,4)$ . Show that this is an isosceles triangle and find the height from $C$ to $AB$ .
29.
A right-angled triangle has legs $a$ and $b$ and hypotenuse $c$ , with $a:b = 3:4$ . If the perimeter is 60 cm, find each side.
30.
Triangle ABC has vertices at $A(1,2), B(5,2), C(3,6)$ . Show that ABC is isosceles and find its area.

PlatinumQuestions 31–40

31.
A triangle has sides 7, 24, 25. (a) Verify it is right-angled. (b) Find the area. (c) Find the height from the right angle to the hypotenuse.
32.
Two similar triangles have sides in ratio 3:4. If the smaller has perimeter 21 cm, find the larger's perimeter. If the smaller has area 9 cm², find the larger's area.
33.
A triangle ABC has $A(0,0), B(8,0), C(4,6)$ . (a) Find each side. (b) Find each angle.
34.
A triangle has angles $A$ , $B$ , $C$ where $A:B:C = 2:3:5$ . Find the angles.
35.
Two triangles have angles (40°, 60°, 80°) and (40°, 60°, 80°). Sides of the first are 5, 6, 8. Sides of the second are 10, 12, 16. (a) Show they are similar. (b) Find the ratio of areas.
36.
A triangle has area 30 cm² and base 10 cm. Find the height. Then find the angles if the triangle is isosceles with the height bisecting the base.
37.
A right-angled triangle has hypotenuse 10 cm and legs $a$ and $b$ , where $a + b = 14$ . Find $a$ and $b$ .
38.
Verify the triangle inequality holds: a triangle has sides $a, b, c$ with $a + b > c$ , $a + c > b$ , $b + c > a$ . If all three are equal, can the triangle still be valid?
39.
A triangle has the angles in the ratio 1:1:2. (a) Find the angles. (b) Show that this is a right-angled isosceles triangle.
40.
Two triangles have sides 4, 5, 6 and 6, 7.5, 9. (a) Are they similar? (b) If yes, find the linear and area scale factors.