Triangle Congruency Theorems

∆ABC and ∆CDA are congruent by the ____ triangle congruency theorem.

• SSS

• SAS

• AAS

• ASA

• SSA

Answer explanation

Both triangles share AC, therefore you can use the Reflexive property!

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

∆JMK and ∆LKM are congruent by the _____ triangle congruency theorem.

• HL

• SAS

• AAS

• ASA

• SSA

Answer explanation

Both triangles share MK by the reflexive property. Ad, the angle is between the two congruent corresponding sides!

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

∆JMK and ∆LKM are congruent by the _____ triangle congruency theorem.

• SSS

• SAS

• AAS

• Not enough information

• SSA

Answer explanation

There is no SSA theorem! That's a bad word spelled backwards! :(

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

∆ABC and ∆EDC are congruent by the _____ triangle congruency theorem.

• SSS

• SAS

• HL

• Not enough information

• SSA

Answer explanation

Use the vertical angles to get a congruent angle pair between the marked sides!

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

∆ABC and ∆EDC are congruent by the _____ triangle congruency theorem.

• SSS

• SAS

• HL

• Not enough information

• SSA

Answer explanation

Use the parallel lines to find the alternate interior angles (in yellow).

Pro Tip: if you the vertical angles (in purple) also, you would have lots of options! You could've used SAS, AAS, ASA!

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

The triangles are congruent by the _____ triangle congruency theorem.

• SSS

• SAS

• ASA

• AAS

• SSA

Answer explanation

Use the reflexive property to show the middle line segment is congruent to itself. Its between the two pairs of marked angles, that's why its ASA.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

The triangles are congruent by the _____ triangle congruency theorem.

• HL

• SSS

• ASA

• AAS

• All of these!

Answer explanation

This diagram could really lead you anywhere! As it was marked, you could say HL.

However, if you use vertical angles (in purple), you could use AAS.

If you then used the triangle angle sum to find the missing angles (in blue), those would be congruent. This would allow you to use ASA or SAS.

If you used the pythagorean theorem, you could show the third side pair congruent (in red). That would allow you to use SSS.

So many options!

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

The triangles are congruent by the _____ triangle congruency theorem.

• Not enough information

• SSS

• ASA

• AAS

• SSA

Answer explanation

I have 1 pair of angles and 1 side pair (with the reflexive property). I would need to know something about another angle pair or another side pair to show these triangles are congruent.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

The triangles are congruent by the _____ triangle congruency theorem.

• Not enough information

• SSS

• ASA

• AAS

• SSA

Answer explanation

Use the parallel lines to find a congruent pair of angles! Corresponding angles are i red. This gives you a congruent pair of sides between two angle pairs... thats ASA!

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

Which one of these is NOT a valid triangle congruency theorem?

• HL

• SSS

• SSA

• AAS

• ASA

Answer explanation

There is no Angle-Side-Side Theorem. It spells a bad word : (

Nor is it valid in reverse: Side-Side-Angle.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5