Class 9 SAS, ASA and AAS Congruence — practice questions with answers
Geometry — Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which set of equal parts makes up the SAS congruence rule?
ATwo sides and the angle between them
BTwo angles and the side between them
CTwo sides and any angle
DAll three angles
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Answer: A) Two sides and the angle between them
SAS: two sides and the INCLUDED angle of one triangle equal two sides and the included angle of the other. With a non-included angle (SSA) the rule fails.
2. You know ∠A = ∠D and ∠B = ∠E. Which side equality gives congruence by ASA (not AAS)?
AAB = DE
BBC = DF
CBC = EF
DAC = DF
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Answer: A) AB = DE
ASA needs the side between the two angles: AB (between ∠A and ∠B) and DE (between ∠D and ∠E). BC = EF or AC = DF would be AAS; BC = DF does not correspond.
3. In a kite ABCD, AB = AD and diagonal AC bisects ∠BAD. If ∠ABC = 100°, what is ∠ADC?
A80°
B100°
C50°
D160°
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Answer: B) 100°
AB = AD, ∠BAC = ∠DAC, AC common → △ABC ≅ △ADC (SAS). By CPCT, ∠ADC = ∠ABC = 100°.
4. P lies on the bisector of ∠BAC. PM and PN are perpendiculars from P to AB and AC. Which rule gives △AMP ≅ △ANP?
AAAS
BASA using AM = AN
CSSS
DSAS
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Answer: A) AAS
∠MAP = ∠NAP (bisector), ∠AMP = ∠ANP = 90°, and AP is common — it is opposite the right angles, not between the two angles. So AAS, and PM = PN.
5. △ABC is equilateral. D, E, F lie on AB, BC, CA with AD = BE = CF. What kind of triangle is DEF?
ARight-angled
BIsosceles but not equilateral
CEquilateral
DScalene
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Answer: C) Equilateral
Each of △ADF, △BED, △CFE has one side equal to AD, another equal to (side − AD), and a 60° angle between them. By SAS all three are congruent, so DF = ED = FE.