# KutaSoftware: Geometry- Congruence And Triangles Part 2 (2023)

## Introduction

Free worksheet at www.kutasoftware.com/freeige.html

Go to ➡️ maemap.com/math/geometry/ ⬅️ for more Geometry information!

Happy learning! 💜

## Content

In this video we're, continuing on with the second page of the congruence and triangles, worksheet picking up where we left off with number nine.

Our directions are to write a statement that indicates that the triangles in each pair are congruent in number nine, I'm going to start by saying, triangle, P, Q, R, that's going to be congruent to triangle, both of them share points, P and Q.

However, this is not a reflection.

So as opposed to saying starting with P and saying, triangle, pqt, I'm going to start with Q and say, triangle, Q, P, D.

So triangle, PQR is congruent to triangle.

Qp D note that this is because angle P is congruent to angle Q.

So I'm starting with writing P.

So my first letter of my other triangle will be Q.

Then my second letter.

And this triangle is q, But Q.

And this triangle is congruent to angle P in this triangle.

So my next angle will be P and then R is congruent to D.

So my last letter, when labeling is R and D let's move on to number 10 and number 10 I'm going to start with triangle, r.

S, t, that triangle is congruent to triangle.

Well, R is congruent to angle.

S.

So where R is first in this triangle, s is going to be first in this triangle, angle.

S, in this triangle is congruent with angle R in the next triangle.

So R is my second letter.

And then where T is my last letter in this triangle that T is congruent with I.

So I have that triangle, rst is congruent to triangle.

S, R I.

B WX that's going to be congruent to let's.

Look at the sides.

The W has one tick mark and W X has two tick marks so I'm going to start with the side with one tick, mark and continue on to the side with two tick marks labeling appropriately.

So here is my side with one tick mark.

And there is my side with two tick marks so CD is congruent to V W and W X is congruent to de so I have triangle.

The WX congruent to triangle, C, D E.

And if you want to double-check with angles, angle B is congruent to angle C angle.

W is congruent to angle D and angle X is congruent to angle.

E let's move on to number 12 and number 12 again, I'll label using the sides.

So we have side st congruent to this side.

And we have side tu congruent to this side because st has one tick.

Mark CD has one tick.

Mark tu has two tick marks and de has tick marks so keeping the letters in order.

So since T is in the middle here, d will be in the middle as well.

So I have triangle.

S, T U is congruent to triangle, C, D, E.

So just remember when labeling triangles, you must keep the labeling in order that's associated with the congruent so angle.

S, congruent to angle C.

S and C are the first letters listed angle, T, congruent to angle, D, T and D are the second letters listed.

And then angle U is congruent to angle E.

Those are the last letters listed let's one to our next set of directions for numbers 13 through 16, we are to mark the angles and sides of each pair of triangles to indicate that they are congruent.

So for number 13, it says, triangle, BDC is congruent to triangle, M LK.

Our first letters are B and M.

So those angles are congruent.

So B is congruent to M our second letters, D and L.

Those angles will be congruent.

So D is congruent to L and I like to show congruence and angles with tick marks so I will do a combination of both.

And lastly, C is congruent to angle K so C and K.

So next segment BD will be congruent to segment M L.

So one tick mark on BD and one tick mark on ml segment, DC will be congruent to segment L k2, tick marks on DC 2, tick marks on LK.

And then lastly, BC will be congruent to M k3, tick marks on BC three, tick marks on MK.

So all my sides and angles are appropriately marked let's.

Move on to number 14.

Number 14, angle G is congruent to angle L angle.

F is congruent to angle K and angle E is congruent to angle M.

And in this problem, when marking my angles I'm, just using the tick, mark method, either way whether you use tick marks, or if you indicate it with three lines either way is fine just as long as you keep it consistent within the problem.

So now, let's mark our sides and I'm going to mark them based on the angles.

So since G is congruent to L and F is congruent to K from G to F that's going to be congruent, and from l, 2k that's going to be congruent, then I'm going to move from my angle with two tick marks to my angle with three tick marks so Fe is congruent to K m.

And then from my angle with three tick marks to my angle with one tick, mark I will have three tick marks on that segment and that's my solution and number 14.

And number 15 angle M is congruent to angle.

S, k is congruent to T and L is congruent to L.

Next I'll leave on my side.

Mk is congruent to s.

T KL is congruent to TL and m/l is congruent to SL and that's my solution and number 15 and number 16 triangle, h IJ is congruent to triangle, j, TS.

So first, I'll, mark, H, then I'll, mark I with two tick marks and then J with three.

So in this triangle, our merc J with one tick, mark tea with two tick marks and s with three tick marks.

So from each I that's going to be one tick, mark, I 2, J will be two tick marks and H J will be three JT will be one tick.

Mark TS will be two tick marks J.

S, will be three tick marks I'll start with my sides side.

C D is congruent to side.

Cd one tick, mark segment DB is congruent to segment DL.

So DB is congruent to DL.

And lastly segment CB is congruent to segment CL.

So CB gets three tick marks and CL gets three tick marks next I'll.

Do my angle C and C are congruent D and D are congruent and B and L are congruent.

And lastly, number 18, however, before I walk you through the answer to this, please remember to like this video and subscribe to my channel all likes and subscriptions are greatly appreciated.

And let me know that you're finding this helpful.

So number 18, we have triangle, ji k, congruent to triangle, j, CD, angle.

J is congruent to angle.

J angle is congruent to angle C.

And that leaves me with D and K being congruent next side, ji or segments.

Ji is congruent to segment JC.

So J I is congruent to segment.

Jc segment.

I K is congruent to segment CD segment.

I k congruent to segment CD.

And then my last sides are also congruent.

So JK is congruent to j D.

And with that answer, we wrap up our triangles and congruence worksheet, hopefully you've already clicked that subscribe button.

But if you haven't here's, a friendly reminder to go ahead and do that also, if you have any questions, leave it in the comment section below and I'll get back to you as soon as I can or just go ahead and leave me a note, letting me know that you found this video helpful.

## FAQs

### What are the triangle congruence criteria answers? ›

What are the triangle congruence criteria? When all three pairs of corresponding sides are congruent, the triangles are congruent. Two triangles with three congruent sides. When two pairs of corresponding sides and the corresponding angles between them are congruent, the triangles are congruent.

What is the Part 2 ASA congruence postulate? ›

Angle-Side-Angle (ASA) Congruence Postulate: If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.

Is there enough information to prove the two triangles congruent? ›

You need at least one pair of congruent corresponding sides to prove two triangles are congruent. If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

What is the SAS congruence postulate answers? ›

The SAS postulate says that if two sides of one triangle and the angle included between them are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

What are the 5 triangle congruence conditions? ›

Two triangles are congruent if they satisfy the 5 conditions of congruence. They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).

What is postulate 2 in geometry? ›

GEOMETRY POSTULATES AND THEOREMS

Postulate 1: Through any two points, there is exactly one line. Postulate 2: The measure of any line segment is a unique positive number. The measure (or length) of AB is a positive number, AB.

What are the four cases of congruence of 2 triangles? ›

SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side)

How do you prove two triangles are congruent using ASA? ›

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Which two Cannot be used to prove 2 triangles are congruent? ›

Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places. Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.

How many pairs of corresponding parts are congruent if two triangles are congruent? ›

Notice that when two triangles are congruent their three pairs of corresponding angles and their three pairs of corresponding sides are congruent.

### How to prove two triangles that are congruent have congruent angles? ›

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.

What is SAS congruence rule simple? ›

SAS Congruence Rule (Side – Angle – Side)

Two triangles are said to be congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

What is SAS postulate easy? ›

There's the Side-Angle -Side postulate, or SAS. This states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

How do you explain SAS in geometry? ›

Side-Angle-Side (SAS) criterion states that if two triangles have two pairs of congruent sides and the included angle in one triangle is congruent to the included angle in the other triangle, then the triangles are congruent.

Is SSA a triangle congruence criteria? ›

SSA congruence rule is also known as side-side-angle congruence rule refers to the congruence of two triangles. Two triangles are said to be congruent when it one of these five conditions are met, SSS, SAS, ASA, AAS, and RHS criteria.

What are the basic congruence criteria? ›

Congruent shapes
• The three sides are equal (SSS: side, side, side)
• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

What are the criteria for triangle congruence postulates? ›

Two or more triangles are congruent if the sides and angles of one triangle are equal to the sides and angles of another triangle. The congruency can also be tested by three postulates shown in the lesson: ASA (angle-side-angle), SAS (side-angle-side), and SSS (side-side-side).

What is a triangle congruence test? ›

The SAS congruence test. If two sides and an include angle of one triangle are respectively equal to two sides and the included angle of another triangle, then the triangles are congruent.

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