- AASA
- BSAS
- CSSS
- DAAS
Step-by-Step Solution
Two angles are marked equal and one side, . That side is not the side between the two marked angles (that would be ), so the rule is AAS, not ASA.
Answer: D) AAS
The arcs and tick marks show which parts of △DEF and △LMN are equal. Which congruence rule proves the two triangles congruent?
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: The four valid congruence criteria
**SSS**: All three sides equal → congruent.
**SAS**: Two sides + included angle equal → congruent.
IMPORTANT: the angle must be BETWEEN the two given sides. SSA (two sides + non-included angle) is NOT a valid criterion in general.
**ASA**: Two angles + included side equal → congruent.
**AAS**: Two angles + a non-included side equal → congruent (since the third angle is forced by 180°).
**RHS** (right triangles only): Right angle + hypotenuse + one side equal → congruent.
**Once congruent, all corresponding parts are equal (CPCT)** — that's the lemma you cite to extract any matching side or angle in the next step of a proof.
**SAS**: Two sides + included angle equal → congruent.
IMPORTANT: the angle must be BETWEEN the two given sides. SSA (two sides + non-included angle) is NOT a valid criterion in general.
**ASA**: Two angles + included side equal → congruent.
**AAS**: Two angles + a non-included side equal → congruent (since the third angle is forced by 180°).
**RHS** (right triangles only): Right angle + hypotenuse + one side equal → congruent.
**Once congruent, all corresponding parts are equal (CPCT)** — that's the lemma you cite to extract any matching side or angle in the next step of a proof.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Triangles (Congruence) practice questions
More Class 9 Triangles (Congruence) practice
Both triangles have a right angle (square marks). Using the tick marks, which rule…The tick marks show that the three sides of △ABC are equal to the three sides of the…In △ABC, AB = AC (tick marks) and AD is perpendicular to BC. If ∠BAD = 28°, find ∠ACB.In △ABC, AB = AC (tick marks). BE ⊥ AC and CF ⊥ AB are altitudes with CF = (2x + 1) cm…In △ABC, ∠A = 48° and ∠B = 67°. Which side of the triangle is the longest?