Question

Problem 1:In the isosceles triangle ABC, BA and BC are congruent. M and N are points on AC such that MA is congruent to MB and NB is congruent to NC. Show that triangles AMB and CNB are congruent.
Problem 2: ABCD is a parallelogram and BEFC is a square. Show that triangles ABE and DCF are congruent.
Problem 3: ABCD is a square. C' is a point on BA and B' is a point on AD such that BB' and CC'are perpendicular. Show that AB'B and BC'C are congruent.

Answer 1

Since triangle ABC is isosceles and BA and BC are congruent then angles BAM and BCN are congruent.

Also since MA is congruent to MB, then AMB is an isosceles triangle and angles BAM and ABM are congruent. NB and NC are also congruent; CNB is an isosceles triangle and angles CBN and BCN are congruent. In fact all four angles BAM, ABM, CBN and BCN are congruent. Comparing triangles BAM and CNB, they have corresponding sides AB and BC congruent, corresponding angles BAM and BCN congruent and corresponding angles ABM and CBN congruent. These two triangles are therefore congruent. This is the ASA congruent case.

Answer 2

Answer:

do not now the answer .... .