Mathematics
In the adjoining figure, AB = AC and AP = AQ. Prove that
(i) △APC ≅ △AQB
(ii) CP = BQ
(iii) ∠APC = ∠AQB.
Answer
(i) In △APC and △AQB we have,
AB = AC (Given)
AP = AQ (Given)
∠PAC = ∠QAB (Common angles)
Hence, by SAS axiom △APC ≅ △AQB.
(ii) As, △APC ≅ △AQB.
We know that corresponding sides of congruent triangles are equal.
∴ CP = BQ.
Hence, proved that CP = BQ.
(iii) As, △APC ≅ △AQB.
We know that corresponding angles of congruent triangles are equal.
∴ ∠APC = ∠AQB.
Hence, proved that ∠APC = ∠AQB.
Related Questions
In the adjoining figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that
(i) △APC ≅ △AQB
(ii) CP = BQ
(iii) ∠ACP = ∠ABQ.
It is given that △ABC ≅ △RPQ. Is it true to say that BC = QR? Why?
"If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent." Is the statement true? Why?
In the adjoining figure, AD = BC and BD = AC. Prove that:
∠ADB = ∠BCA and ∠DAB = ∠CBA.
