Question

1. In ∆ABC and ∆DCB, AC = BD, ABC = DCB = 90º. Are the triangles congruent ? State the
condition of congruency.
2 A line segment AB is bisected at point P and through point P another line segment PQ,
which is perpendicular to AB, is drawn. Show that : QA = QB.
3 In the following diagram, AP and BQ are equal and parallel to
each other.
Prove that :
(i) ∆AOP ∆BOQ
(ii) AB and PQ bisect each other.

help me

Answer 1

Answer:

We have to state the correspondence between the vertices, sides and angles of the following pairs of congruent triangles.(i) △ABC≅△EFDCorrespondence between vertices:   A↔E, B↔F, C↔DCorrespondence between sides:  AB=EF, BC=FD,CA=DECorrespondence between angles:  ∠A=∠E,∠B=∠F,∠C=∠D(ii)△CAB≅△QRPCorrespondence between vertices:C↔Q, A↔R, B↔PCorrespondence between sides:CA=QR, AB=RP, BC=PQCorrespondence between angles:∠C=∠Q, ∠A=∠R, ∠B=∠P(iii) △XZY ≅△QPRCorrespondence between vertices:X↔Q, Z↔P, Y↔RCorrespondence between sides:XZ=QP, ZY=PR, YX=RQCorrespondence between angles:∠X=∠Q, ∠Z=∠P, ∠Y=∠R(iv)△ MPN≅△SQR

Step-by-step explanation: