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Congruent Triangles Proof

Practice Quiz

The quiz below will test your knowledge of all the postulates and theorems that can prove two triangles are congruent.

Problem 1

Which postulate/theorem that proves congruent trianlges could be used to prove that triangle symbol BAC congruent triangle symbol DEC?

triangle

You could use Angle Angle Side because angle symbol ACB and angle symbol DCE are vertical angles.

The trick, of course, is that you cannot use SSA since SSA(Side Side Angle) is not a valid theorem that proves congruent tirangles.

Problem 2

Which postulate/theorem that proves congruent trianlges could be used to prove that triangle symbol ABC congruent triangle symbol FED? (Use both the stated given as well as the markings on the picture of the triangles).

triangle

The two triangles are congruent by SAS, the side angle side postulate. You'd need to use the addition property of equality to get one pair of the sides.

Problem 3

Which postulate/theorem that proves congruent trianlges could be used to prove the 2 triangles pictured below are congruent

SSS

Since all 3 sides are congruent, we can use the Side Side Side postulate.

Practice problem 3
Problem 4

Which postulate/theorem that proves congruent trianlges could be used to prove the 2 triangles pictured below are congruent

AAS

The AAS postulate states that these 2 triangles are congruent.

Practice problem 4
Problem 5

Which postulate/theorem that proves congruent trianlges could be used to prove the 2 triangles pictured below are congruent

NONE

As the animation below shows, there is no way to prove these 2 triangles are congruent. That is why there is no SSA postulate.

Practice problem 4
Problem 6

Which postulate/theorem that proves congruent trianlges could be used to prove the 2 triangles pictured below are congruent

Hypotenuse Leg

The Hypotenuse Leg states that these 2 triangles are congruent.

Practice problem ASA
Problem 7

Which postulate/theorem that proves congruent trianlges could be used to prove the 2 triangles pictured below are congruent

ASA

The AAS postulate states that these 2 triangles are congruent.

Practice problem ASA
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