Proving Triangles Congruent Using Definition of Congruent Triangles – Part 2

Part 1 of Congruent Figures 4.1

Part 2 of Congruent Figures Proving Triangles Congruent

The third part of this series about congruent figures is proving triangles congruent. At this point, there is only one way to prove triangles congruent, with the definition of congruent triangles. Congruent triangles have 3 pairs of corresponding angles and 3 pairs of congruent angles. So, to prove two triangles congruent, we must establish that all 3 pairs of corresponding sides and angles are congruent.

Given: segment WX is congruent to YX, segment WZ is congruent to segment YZ, angle W is congruent to angle Y and segment XZ is perpendicular to segment WY

Prove: triangle WXZ is congruent to triangle YXZ

Proving Triangles Congruent Diagram 4.1

With the given information: segment WX is congruent to YX, segment WZ is congruent to segment YZ, angle W is congruent to angle Y and segment XZ is perpendicular to segment WY, prove triangle WXZ is congruent to triangle YXZ. First, segment XZ is congruent to segment XZ by the reflexive property of congruence. Angles XZW and XZY are right angles by the definition of right angles. Angle XZW and angle XZY are congruent because all right angles are congruent. Angle WXZ is congruent to angle YXZ by the third angle theorem. It can be established that triangle WXZ is congruent to triangle YXZ by the definition of congruent triangles.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: