Congruent Triangles: Fluency and Exam Drill - Worksheets, Questions and Revision

12 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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7.14D Congruent Triangles: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Triangles ABC and DEF have AB = DE, BC = EF and AC = DF. Which congruence test proves the triangles are congruent?
(Total for Question 1 is 1 mark)
2
Triangles PQR and STU satisfy PQ = ST, PR = SU and angle QPR = angle TSU where the equal angle is between the equal sides. Which congruence test applies?
(Total for Question 2 is 1 mark)
3
Two right-angled triangles have equal hypotenuses and one pair of equal legs. Which congruence test proves they are congruent?
(Total for Question 3 is 1 mark)
4
Triangles XYZ and LMN have angle X = angle L, angle Z = angle N and the side XZ = LN between those angles. Which congruence test applies?
(Total for Question 4 is 1 mark)
5
Triangles ABC and PQR are congruent with the correspondence A-P, B-Q, C-R. AB = 8, BC = 12 and CA = 10. Work out QR.
(Total for Question 5 is 2 marks)
6
Triangle ABC is right-angled at B with AB = 5, BC = 12 and AC = 13. Triangle DEF is right-angled at F with EF = 5 and DE = 13. Use congruence to find DF (labelled x in the second triangle).
(Total for Question 6 is 3 marks)
7
Triangles ABC and DEF satisfy angle A = 50 degrees, angle C = 70 degrees and AC = DF. In triangle DEF, angle D = 50 degrees and angle F = 70 degrees. Show that the triangles are congruent and state two pairs of corresponding equal sides.
(Total for Question 7 is 3 marks)
8
In triangle ABC, AB = AC and D is the midpoint of BC so BD = DC. Show that triangles ABD and ACD are congruent. Hence state angle ABD = angle DCA.
(Total for Question 8 is 4 marks)
9
Quadrilateral ABCD has AB = CD and BC = DA. The diagonal AC is drawn. Prove that triangles ABC and CDA are congruent, and hence state one pair of equal corresponding angles.
(Total for Question 9 is 4 marks)
10
In triangle ABC, AB = 7 cm, AC = 9 cm and angle BAC = 60 degrees. Triangle DEF has DE = 7 cm, DF = 9 cm and angle EDF = 60 degrees. (a) Show that triangles ABC and EDF are congruent. (b) Work out the length BC, giving your answer to 3 significant figures.
(a)Show that triangles ABC and EDF are congruent.(2)
(b)Work out BC to 3 significant figures.(3)
(Total for Question 10 is 5 marks)
11
Triangles ABC and DEF satisfy AB = DE, angle B = angle E and BC = EF. (a) State the congruence test that proves the triangles congruent. (b) Using the congruence, state two pairs of corresponding equal angles.
(a)State the congruence test.(2)
(b)State two pairs of corresponding equal angles.(4)
(Total for Question 11 is 6 marks)
12
In quadrilateral ABCD, AB = CD and BC = DA. The diagonal AC is drawn. Prove that triangles ABC and CDA are congruent by SSS and state which pair of corresponding angles are equal as a result.
(Total for Question 12 is 5 marks)
Mark scheme · 7.14D Congruent Triangles: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12