Question

AD is the altitude of an equilateral triangle ABC. Is ΔADB ≅ ΔADC? If so,
state the congruence criteria used.

Answer 1

Answer:

ABC is an isosceles triangle with AB = AC and AD is one of its altitudes.

congruent triangles

State the three pairs of equal parts in ΔADB and ΔADC.

Answer: AD = AD, AB = AC and DB = DC

Is ΔADB ≈ ΔADC? Why or why not?

Answer: By SSS criterion, triangles are congruent.

Is angle B = angle C? Why or why not?

Answer: Yes, because they are included between equal sides of given congruent triangles.

Is BD = CD? Why or why not?

Answer: Yes, because altitude of an isosceles triangle bisects its base when the base is not one of the two equal sides.