Triangle Proof Practice

What conclusion can we make, using the given information of a bisector?

Answer explanation

Here, it is a segment that is being bisected, specifically the one that comes after the word "bisects." This means we want to make a conclusion about the smaller segments formed from that segment.

Tags

CCSS.HSG.CO.C.9

What information can we determine from the picture, since we have used all the given information already?

Answer explanation

We do not have a shared side between these triangles, so when looking at the figure, we can only look for vertical angles and use the vertical angles theorem to know they are congruent.

Tags

CCSS.HSG.CO.C.9

Why are the triangles congruent?

• SAS Congruence

• ASA Congruence

• AAS Congruence

• HL Congruence

Answer explanation

We have two angles and the included side marked congruent in each triangle.

Tags

CCSS.HSG.SRT.B.5

Since we are given parallel lines in the triangles, what type of object should we look for to be congruent?

• Sides

• Angles

• Triangles

• Rays

Answer explanation

Parallel lines create congruent angle pairs, which is what we look for in each triangle.

Tags

CCSS.HSG.SRT.B.5

• Vertical Angles Theorem

• Corresponding Angles Theorem

• Definition of Bisect

• Alternate Interior Angles Theorem

Answer explanation

These angles are formed by the parallel lines and the transversal through point A and point E. They are in an alternate interior position, and they are angles in each triangle.

Tags

CCSS.8.G.A.5

What is something we can determine from the figure, without using any of the given information?

• Congruent Sides

• Perpendicular Lines

• Congruent Angles

• Angle Bisectors

Answer explanation

For these triangles, since they do not share a side, the only thing we could pick out from the figure would be congruent angles (if there are vertical angles--which there are!).

Tags

CCSS.HSG.CO.C.9

Which angles are congruent using the Vertical Angles Theorem?

Answer explanation

Make sure your vertical angles have the same point as the vertex of the angle, and that they are named so that corresponding parts match up!

Tags

CCSS.HSG.SRT.B.5

• SAS Congruence

• SSS Congruence

• AAS Congruence

• ASA Congruence

Answer explanation

Two angles and the included side in each triangle are marked as being congruent.

Tags

CCSS.HSG.SRT.B.5

• Reflexive POC

• ASA Congruence

• CPCTC

• Definition of Congruent

Answer explanation

Once two triangles are congruent, we know that Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Tags

CCSS.HSG.SRT.B.5