Question

Determine which postulate or theorem can be used to prove that ABC=DCB.

A. AAS
B. SAS
C. SSS
D. ASA

Answer 1

Postulate (statement that is taken to be true) or theorem that can be used to prove that ABC=DCB is A. AAS

Explanation:

The triangle is a polygon any 2-dimensional shape formed with straight lines) consist of the three edges and three vertices. It is one of the basic shapes in geometry.  In triangle of ABC and triangle of DBC given the ∠A=∠D and ∠B=∠C

Then each of triangle that being 90° given in the diagram.

∠ABC=∠DCB

Then Δ ABC ≅ ΔD BC

When two triangles are congruent, then their areas are equal. Therefore, Area (ABC) = Area (DCB)

Therefore A. AAS postulate or theorem can be used to prove that ABC=DCB.

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The other example can be seen in the second attachment of picture. The question is still the same: Determine which postulate or theorem can be used to prove that ABC = DCB!

Then AC = DB

AB = DC

BC = BC, This side is equal to itself

Therefore the three sides of one triangle equal to 3 sides of the other. It means that the triangles are congruent. Therefore the answer is SSS

Hope it helps you to learn more about triangle.

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Answer 2

Answer:

A. SAS

Step-by-step explanation:

In the figure attached, the triangles are shown.

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In this case, the two sides of triangle ABC are AC and BC and the included angle is ∠C, which are congruent with sides BD and BC and the included angle ∠B from triangle BCD