Which of the following pairs of triangles are congruent by ASA condition?

Question

Which of the following pairs of triangles are congruent by ASA
condition?

Global Expert · Accepted Answer

1) We have

Since ∠ABO = ∠CDO = 45° and both are alternate angles,  AB∥DC∠BAO = ∠DCO  (alternate angle , AB∥CD and AC is a transversal line)∠ABO = ∠CDO = 45° (given in the figure) Also, AB = DC    (Given in the figure)Therefore, by ASA △AOB ≅△DOC

2)
In △ABC ,Now AB = AC (Given)∠ABD = ∠ACD = 40° (Angles opposite to equal sides)∠ABD +∠ACD+∠BAC=180° (Angle sum property)40°+40°+∠BAC=180°∠BAC=180°-80°=100°∠BAD +∠DAC=∠BAC∠BAD=∠BAC-∠DAC=100°-50°=50°∠BAD =∠CAD = 50°Therefore, by ASA, △ABD ≅△ADC
3)
In∆ABC,∠A+∠B+∠C=180°(Angle sum property)∠C=180°-∠A-∠B∠C=180°-30°-90°=60°In∆PQR,∠P+∠Q+∠R=180°(Angle sum property)∠P=180°-∠Q-∠R∠P=180°-60°-90°=30°∠BAC = ∠QPR = 30°∠BCA=∠PRQ = 60°and AC = PR (Given)Therefore, by ASA, △ABC ≅△PQR

4)
We have only BC =QR  but none of the angles of △ABC AND △PQR are equal
Therefore, △ABC≇ △PRQ