- A62°
- B48°
- C70°
- D110°
Step-by-Step Solution
Matching the ticks: , so (SSS). By CPCT, .
Answer: C) 70°
The tick marks show that the three sides of △ABC are equal to the three sides of the second triangle (same number of ticks = equal sides). ∠B = 62° and ∠C = 48°. Find the angle marked ? at R.
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.
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