Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Two triangles share the side PQ. What reason do you write?
Show worked solution
PQ is common.
2 Can you claim two sides are equal because they look equal in the diagram?
Show worked solution
No — you must be given it or prove it.
3 What must you name at the end of a congruence proof?
Show worked solution
The test used.
Level 2 · Core
4 M is the midpoint of BC. What equality does this give you?
Show worked solution
BM = CM.
5 In △ABM and △ACM you have AB = AC, BM = CM and AM common. Which test applies?
Show worked solution
SSS — all three are sides.
6 You have proved △ABM ≡ △ACM. What reason lets you say ∠ABM = ∠ACM?
Show worked solution
Matching angles of congruent triangles are equal.
Level 3 · Challenge
7 Two triangles are formed by two crossing straight lines. What angle fact does the crossing give you?
Show worked solution
Vertically opposite angles are equal.
8 A diagram marks two lines with arrows (parallel). What kind of equal angles might this give?
Show worked solution
Alternate or corresponding angles.
9 After writing "∴ △ABD ≡ △CBD (SSS)", what should the NEXT line do?
Show worked solution
State the fact you were asked to prove, with the reason "matching sides/angles of congruent triangles are equal".