Use the diagram. Given: P S=R Q, m ∠1=m ∠4 Prove: m ∠3=m ∠2 CAN'T COPY THE FIGURE

Name: Problem 19, Chapter 4: Geometry
Uploaded: 2020-04-30T15:38:27-08:00
Duration: 5 min 9 s
Channel: Dawn Getman
Description: Use the diagram. Given: P S=R Q, m ∠1=m ∠4 Prove: m ∠3=m ∠2 CAN'T COPY THE FIGURE

step 1 We're looking at question 19, which is a proof. And I'm going to set it up as a two -column proo

Use the diagram. Given: P S=R Q, m ∠1=m ∠4 Prove: m ∠3=m ∠2...

Key Concepts

Triangle Congruence

This concept involves showing that two triangles are congruent by using criteria such as Angle-Side-Angle (ASA) or Side-Angle-Side (SAS). Once congruence is established, it guarantees that all corresponding sides and angles are equal, which is a powerful tool in geometric proofs.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

After establishing the congruence of two triangles, CPCTC allows us to conclude that every pair of corresponding sides and angles are congruent. This property is often used to prove that particular angles or segments within the figure are equal.

Angle Relationships

Understanding how angles relate to one another in geometric figures is crucial. In many proofs, given angle equalities (such as between alternate interior angles or vertically opposite angles) lead to further angle relationships within congruent figures, aiding in demonstrating that specific angles are equal.

Transcript

00:04 We're looking at question 19, which is a proof.

00:07 And i'm going to set it up as a two -column proof, but you could also do a flow proof or paragraph proof or whatever style of proof that you've been using in class.

00:20 And we'll fill in our statements and reasons.

00:30 And with this one, we have the same diagram for several proofs.

00:33 So one of the things to keep in mind is diagrams are not always drawn to scale.

00:37 So if things don't look equal, but you're told they're equal, you know.

00:41 They're equals.

00:42 So keep that in mind.

00:44 So our statements for the beginning, and with proof, you can do a couple different ways for two column proofs.

00:50 One way is to do all the statements and then list all the reasons.

00:54 Another is to do statements and reasons together.

00:56 I do it both ways.

00:58 Today i'm going to do the statements first and then the reasons.

01:00 So we're going to start with our given, which is ps is equal to our q, and the measure of angle one equals the measure of angle four.

01:23 And we're trying to prove that the measure of angle three equals the measure of angle two.

01:29 So what we want to do is get the triangles congruent.

01:32 If we can get the triangles congruent, then we can use corresponding parts to get that prove statement that we want.

01:41 So some teachers would let you just use these and imply that they're congruent.

01:45 Some teachers like the formality of changing it over.

01:47 So i'm going to change it over in case you have a formal teacher.

01:51 You could skip this step or these steps actually if your teacher doesn't make you convert to congruence.

01:58 So for the first one, we know that pq is or p .s is congruent to rq because they were equal.

02:05 And then the same thing for step three, the angle one is going to be congruent to angle four because they were equal in the given.

02:17 And that gives us a side and an angle.

02:20 So we need one more either side or angle.

02:23 And since they share the side qs, we know that qs is congruent to qs by the reflexive property...

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