Question

E) Observe the figure and state the three pair of equal parts in triangles ABC and DCB.
a) Is ∆ABC = ∆DCB? Why?

b) Is AB = DC? Why?
c) Is AC = DB? Why?​

Answer 1

Answer:

Three pairs of equal parts in ∆ABC and ∆DCB

Three pairs of equal parts in ∆ABC and ∆DCBare angle ABD and angle DCA, angle ACB and angle DBC ,BC and BC

Step-by-step explanation:

a) In ∆ACB and ∆DBC ( By figure )

Angle ABC = Angle DCB (In both 30°+40° = 70°)

BC = BC ( common)

∆ACB and ∆ DBC are congruent by ASA theorem

b) Hence AB=DC ( Congruent parts of congruent triangles )

c) Hence Ac=DB ( Congruent parts of congruent triangles) .

If you are helped, mark as brainliest. Thanks .

Answer 2

hi

Step-by-step explanation:

Considering triangles ABC and DCB,

∠ABC = ∠DCB = 70°

Common side = BC

∠ACB = ∠DBC = 30°

ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".

By ASA rule, ∆ABC ≅ ∆DCB.

Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.

Considering triangles ABC and DCB,

By CPCT,

AB = DC

AC = DB