Question

Which postulate or theorem, if any, could be used to prove the triangles congruent? If not enough information is given, write not enough information.

Answer 1

Two triangles are congruent if and only if they have the same shape and size. So, there are several ways to find out if two triangles are congruent, so we will study the triangles above to find the answers:

Case a. (AAS - Angle, Angle, Side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal. So, for the figure above it is true that:

$\overline{AC}=\overline{DF}$
∠B = ∠E
∠A = ∠D

Case b. We don't have any information about this case that allows us to get a conclusion about congruence. Recall that for congruent triangles you need to compare three elements two by two.

Case c. (SSS - Side, Side, Side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. So, for the figure:

$\overline{AB}=\overline{ED}$
$\overline{AC}=\overline{DF}$
$\overline{BC}=\overline{EF}$

Case d. We only have two equal elements, but it is necessary to have three elements for comparing them doing the comparison two by two. There is not enough information for getting a conclusion.

Answer 2

Question 11a)
We are given side BC equals to side CE and angle CBA equals to angle CEDWe also know that angle ACB equals to angle ECD are equal (opposite angles properties)
We have enough information to deduce that triangle ABC and triangle CDE are equal by postulate Angle-Side-Angle (ASA)
---------------------------------------------------------------------------------------------------------------
Question 11b)
We are given side AB equal to side ED, side BC equals to side EF, and side AC equals to side DFWe have enough information to deduce that triangle ABC and triangle DEF congruent by postulate Side-Side-Side (SSS)
----------------------------------------------------------------------------------------------------------------
Question 11c)
We are given side AC equals to side DF, angle ABC equals to angle DEF, and angle BAC equals to angle EDF
We have enough information to deduce that triangle ABC congruent to triangle DEF by postulate Angle-Side-Angle (ASA)
-----------------------------------------------------------------------------------------------------------------
Question 11d)
We do not have enough information to tell whether this shape congruent or not