Given: Q R S is adjacent to Q T S . Q S bisects ∠R Q T . ∠R ≅∠T Prove: Q S bisects R T.

Name: Problem 14, Chapter 4: Geometry
Uploaded: 2020-04-29T16:31:47-08:00
Duration: 7 min 33 s
Channel: Dawn Getman
Description: Given: Q R S is adjacent to Q T S . Q S bisects ∠R Q T . ∠R ≅∠T Prove: Q S bisects R T.

step 1 Hi, we're looking at question 14, and this one doesn't have a diagram. It just gives us the give

Given: Q R S is adjacent to Q T S . Q S bisects ∠R Q T . ∠R...

Key Concepts

Corresponding Parts of Congruent Triangles (CPCTC)

Once two triangles are proven congruent, the Corresponding Parts of Congruent Triangles (CPCTC) theorem states that all corresponding sides and angles are equal. This concept is often used to conclude that a particular segment or angle is bisected or equivalent to another, thereby finalizing the proof through established equality.

Triangle Congruence

Triangle congruence is a principle that allows us to prove that two triangles are identical in shape and size if they meet specific criteria such as ASA, AAS, SSS, or SAS. Establishing triangle congruence is crucial in many geometric proofs because it allows us to deduce that corresponding angles and sides are equal.

Angle Bisector

An angle bisector is a line or ray that divides an angle into two congruent angles. This concept is fundamental in geometry as it is used to establish symmetrical relationships within triangles and other figures, often leading to proportional relationships between segments.

Transcript

00:03 Hi, we're looking at question 14, and this one doesn't have a diagram.

00:08 It just gives us the given.

00:09 So i'm going to start by making a diagram, and we want to look through our given.

00:12 We know that we have triangle qrs is adjacent to triangle qts.

00:17 And since we see that both have q and s, we know they're going to share aside.

00:21 We know that qs bisex angle rqt, so there must be some kind of angle that qs is going through.

00:29 And we know we're trying to prove that qs bisex r2.

00:34 So with all of that in mind, we're looking at a diagram that's going to look something like this.

00:41 And this is going to be our r and our t on one side or the other.

00:47 And then here would be our q and then there would be a side here that they share.

00:54 So now you can see.

00:56 And whenever you do a sketch yourself, always go back and look and see.

01:00 Is triangle qrs adjacent to triangle qts? yes, they're next to each other.

01:05 Whether they touch.

01:06 Qs, they tell us bisects.

01:08 So here we can actually mark our diagram.

01:10 Qs bisex angle rqt.

01:13 So this big angle is angle rqt.

01:16 And since qs bisects it, these two parts are gonna be equal, and then it tells us that angle r is congruent to angle t.

01:27 So that's what i'm looking at for my proof.

01:31 I'm going to start with my given.

01:34 I'm gonna do a two column proof.

01:37 So you should have, so up here should be statements.

01:45 I'll squish it in here.

01:48 It should be on top, but my screen's kind of running out of room there.

01:53 So statements and then reasons.

01:56 And the reasons i'm actually going to type at the end, you can do the reasons as you go as well.

02:02 So sometimes i do that where i do the statement and reason together.

02:06 And sometimes i do the statement at first and do all statements and then go back and fill in the reasons.

02:11 So our first statement is just our given.

02:14 And some people like to put the given in as they need it, and others like to put it all at the top.

02:19 I'm a top person.

02:22 So triangle qrs is adjacent to triangle qts.

02:36 And that we mostly need to know for the picture.

02:38 It's not really going to help us in our proof to be able to get our picture there.

02:44 And then qs biceps, and this we will need.

02:47 As a matter of fact, we marked the picture, and we need to make sure that we put that part in our proof about those congruent angles.

02:55 So qs bisex angle rqt, and then it also tells us that angle r is congruent to angle t, which we will need later.

03:23 So the next step that i would always tell my students to do, since you mark the two angles congruent that make up angle rqt, is to actually state that congruence...

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