Can You Use the Sss Postulate or the Sas Postulate to Prove

Did you know that at that place are five ways you can prove triangle congruency?

Jenn, Founder Calcworkshop^®, fifteen+ Years Experience (Licensed & Certified Teacher)

It's truthful!

In today's geometry lesson, we're going to tackle two of them, the Side-Side-Side and Side-Angle-Side postulates.

Yous'll quickly learn how to prove triangles are congruent using these methods.

In improver, you lot'll see how to write the associated ii cavalcade proof.

Let'southward spring in!

So we already know, two triangles are coinciding if they have the same size and shape. This means that the pair of triangles have the same three sides and the same 3 angles (i.e., a total of six corresponding congruent parts).

Thankfully we don't need to prove all 6 respective parts are coinciding… we just need three!

Why?

Because if we can evidence specific sides and/or angles to be coinciding betwixt a pair of triangles, then the remaining sides and angles are besides equal.

But in that location is a alert; we must exist conscientious virtually identifying the accurate side and angle relationships!

As Math is Fun accurately states, at that place but five unlike congruence postulates that volition work for proving triangles congruent. So we need to learn how to place coinciding corresponding parts correctly and how to utilize them to prove two triangles congruent.

Triangle Congruence Postulates

The beginning ii postulates, Side-Bending-Side (SAS) and the Side-Side-Side (SSS), focus predominately on the side aspects, whereas the next lesson discusses 2 boosted postulates which focus more on the angles. Those are the Angle-Side-Bending (ASA) and Angle-Angle-Side (AAS) postulates.

Side-Angle-Side

If we can bear witness that two sides and the included angle of one triangle are congruent to two sides and the included bending in a second triangle, and so the 2 triangles are congruent.

This is called the Side Angle Side Postulate or SAS. And as seen in the epitome, we prove triangle ABC is congruent to triangle EDC by the Side-Angle-Side Postulate

SAS Postulate Instance

Side-Side-Side

Or, if we tin determine that the three sides of one triangle are coinciding to iii sides of another triangle, then the ii triangles are congruent.

We refer to this every bit the Side Side Side Postulate or SSS. And every bit seen in the paradigm to the right, we evidence that trianlge ABC is congruent to triangle CDA by the Side-Side-Side Postulate.

SSS Postulate Example

I'thousand confident that after watching this lesson y'all will agree with me that proving triangles congruent is fun and straightforward.

Triangle Congruency – Lesson & Examples (Video)

38 min

• Introduction to triangle congruency lesson
• 00:00:13 – What are SAS and SSS Postulates?
• 00:07:twenty – Are the triangles coinciding by SAS? (Examples #1-iii)
• Sectional Content for Member's Only

• 00:13:58 – Are the triangles congruent by SSS? (Examples #4-6)
• 00:18:12 – Write SAS, SSS or Not Coinciding (Examples #7-12)
• 00:32:twenty – Complete the two-column proof (Example #xiii)
• Practice Issues with Step-by-Footstep Solutions
• Affiliate Tests with Video Solutions

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Source: https://calcworkshop.com/congruent-triangles/sss-sas-postulates/

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