Congruence, Similarity & Geometrical Proof Practice Questions

Two of these triangles are congruent.

Write down the letters of these two triangles.

............................ and ............................

Two of these triangles are similar but not congruent.

Write down the letters of these two triangles.

............................ and ............................

A small rectangular picture frame is $12$ cm wide and $18$ cm high.

A larger picture frame is mathematically similar to the small frame.

The larger frame is $20$ cm wide.

Work out the height of the larger frame.

....................................................... cm

Each row of the table gives some information about a pair of triangles.

In each row, the information given is enough to show that the two triangles are congruent.

Complete the table. Choose your answer from SSS, SAS, ASA and RHS.

	Information given	Congruence condition
(i)	In triangles $ABC$ and $PQR$: $AB = PQ = 6$ cm, angle $A$ = angle $P$ = $55°$, $AC = PR = 9$ cm	............................
(ii)	In triangles $DEF$ and $STU$: angle $D$ = angle $S$ = $40°$, $DE = ST = 7$ cm, angle $E$ = angle $T$ = $75°$	............................
(iii)	In triangles $KLM$ and $XYZ$: angle $L$ = angle $Y$ = $90°$, $KM = XZ = 13$ cm, $LM = YZ = 5$ cm	............................

Write down the side of triangle $EDC$ that corresponds to side $AB$.

.......................................................

Work out the length of $DE$.

....................................................... cm

Prove that triangle $ABC$ is congruent to triangle $CDA$.

Give a reason for each statement you make.

Hence write down the length in the diagram that is equal to $BC$, giving a reason for your answer.

Explain why triangle $ADE$ and triangle $ABC$ are similar.

Work out the length of $BC$.

....................................................... cm

Work out the length of $EC$.

....................................................... cm