Question

Which criterion can be used to prove abc and adc are congruent? triangles, abc and acd, are plotted on a grid that share a common side ac. angles cad and acb are marked congruent. angles cab and acd are marked congruent. a. sss b. aaa c. sas d. asa

Answer 1

The correct answer is option D which is ASA ( Angle - Side - Angle).

What is congruency?

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In triangles ABC and ADC,

Angles BCA and DAC are congruent (from the diagram);

Angles BAC and DCA are congruent (from the diagram);

AC is congruent AC (by reflexive property).

So, the triangles ABC and CDA are congruent with the ASA postulate.

ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Therefore the correct answer is option D which is ASA ( Angle - Side - Angle).

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