10. 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. Justify your answer in each case.
Tick one box only for each statement Statement (i) (ii)
If two angles in a triangle are equal, the triangles are congruent.
If two triangles are congruent, then their corresponding sides are equal in length.
(iii) Angle-angle-angle (AAA) is a condition for congruency. (iv) An isosceles triangle and a scalene triangle can be congruent to each other
(v)
If two triangles are equilateral, then they are congruent to each other.
(vi) Right-angled triangles are congruent to each other.
11. Given the isosceles triangle XYZ opposite, where |XY| = |YZ| and W is the midpoint of |XZ|, show that ∆WXY is congrugent to ∆WZY by:
(i) side-side-side (SSS) (ii) side-angle-side (SAS)
Y
Always true
Sometimes true
Never true
X
W A
12. The triangle ABC is shown on the right. Find the value of x, given the traingles ACR and ABR are congruent.
4x + 8 7x – 4
Z
C
R
13. Mark constructs a triangle using an online geometry tool. He tells Alice that his triangle has an angle of 49° and sides of lengths 3·6 cm and 7·1 cm.
With only this information, will Alice be able to construct a triangle that is congruent to Mark’s triangle?