2. Construct a right-angled triangle ABC with |AB| as the hypotenuse when: (i)
|AB| = 6 cm and |BC| = 4 cm |AB| = 5·5 cm and |BC| = 4·5 cm (iii) |AB| = 10 cm and |BC| = 6·5 cm
(ii)
3. Construct triangles using the rough sketches below: (i)
(ii) (iii) (iv)
4. Construct a right-angled triangle ABC with |AB| as the hypotenuse when: (i)
|AB| = 9·5 cm and |∠CAB| = 47° |AB| = 8·5 cm and |∠BAC| = 38° (iii) |AB| = 7·5 cm and |∠CAB| = 56°
(ii)
5. Copy the table below and put a tick (✓) in the correct box in each row to show whether each statement is always true, sometimes true, or never true, for any triangle.
Statement (i) (ii)
It is possible to construct a triangle with two 90° angles.
It is possible for a triangle to be both a right-angled triangle and isosceles.
(iii) It is possible for a triangle to be both a right-angled triangle and equilateral.
(iv) If a triangle is right-angled, the other two angles add up to less than 90°.
15·6 Interior and exterior angles in triangles
An exterior angle is the angle between any side of a shape, and a line extended from the adjacent side.
An interior angle is an angle inside a shape. Tick one box only for each statement Always true Sometimes true Never true
By the end of this section you should be able to: ● identify the interior and exterior angles in a triangle ● find the measure of exterior angles in a triangle
When we add an interior angle to an adjacent exterior angle, we get a straight line measuring 180°. Therefore, these are called supplementary angles.