Proving Triangles Congruent Using Definition of Congruent Triangles

The second part of this series about congruent figures is proving triangles congruent. If you are interested in the reading the first post on Congruent Figures. 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. The third angle theorem states, if two angles of one triangle are congruent to two angles of another triangle, the third angles are congruent to each other.

Given: segment AB is congruent to segment AD, segment BC is congruent to segment DC, angle B is congruent to angle D, and angle BAC is congruent angle DAC

Prove: triangle ABC is congruent to triangle ADC

Proving Triangles Congruent Section 4.1

Prove Triangle ABC congruent to Triangle ADC

With the given information: segment AB is congruent to segment AD, segment BC is congruent to segment DC, angle B is congruent to angle D, and angle BAC is congruent angle DAC, prove triangle ABC is congruent to triangle ADC. Segment AC is congruent to segment AC by the reflexive property of congruence. Next, it must be established that angle ACB is congruent to angle ACD, by the third angle theorem. Since, all three pairs of corresponding sides and angles are congruent, triangle ABC is congruent to triangle ADC.

Advertisements

4 Responses

  1. […] Proving Triangles Congruent Using Definition of Congruent Triangles […]

    • iam of 8std.i needed an video on concruent triangles.so please can you help me?……………………..

  2. what is the difference between the congruency and concurrency?

    • In geometry, there is no such thing as congruency. Shapes are congruent or not congruent. This is a commonly misused word in geometry.

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: