Triangle Congruency

4.3 Notes - Congruent Triangles

Answer this question on your notes then you will type in your answers on the next few slides.

Multiple Choice

Angle X is congruent to Angle

• E

• F

• G

Answer this question on your own. You will enter answers in on the next few slides.

Multiple Choice

measure of Angle H=

• 38

• 71

Multiple Choice

FD =

• KI

• IK

• JK

• KJ

Multiple Choice

Angle A = ?

• L

• M

• N

Multiple Choice

ANGLE U = ANGLE ?

• E

• F

• G

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Poll

How comfortable are you with congruency statements?

• No problem!

• It's OK!

• I don't get it.

​Ways to Prove Triangles are Congruent

Complete the foldable on page 52 with this quizizz! Both are a grade!

​This means that all 3 sides are congruent.

​​Side-Side-Side

​

​This means the 2 sides are congruent as well as the angle between them. (Order matters)

​​Side-Angle-Side

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​This means the 2 angles are congruent as well as the side between them. (Order matters)

​​Angle-Side-Angle

​This means the 2 angles are congruent as well as the side beside (not between) one of the angles. (Order matters)

​​Angle-Angle-Side

​

​There are 4 Triangle Theorems that are used to prove that triangles are congruent.

​STOP!!! Complete these notes on the top of page 52. Markings are important!

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • Segment GH ≅​ Segment JI (Side) -> This is given to us by the single markings on each line.

  • We also know that Segment JH ≅ Segment JH (Side)because they are the same line.

  • Lastly, since GH and JI are parallel, we know that ∠GHJ ≅​ ∠IJH (Angle) because they are alternate interior angles.

​

​STOP! Example 1 inside foldable.

Therefore, since 2 sides are congruent and the angle between them is congruent, this is Side-Angle-Side

​

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • Segment PQ ≅​ Segment PS (Side) -> This is given to us by the single markings on each line.

  • Segment QR ≅​ Segment SR (Side) -> This is given to us by the double markings on each line.

  • We also know that Segment PR ≅ Segment PR (Side) because they are the same line.

​

​STOP! Example 2 inside foldable.

Therefore, since all 3 sides are congruent, this is Side-Side-Side!

​

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • ∠B ≅​ ∠D (Angle) -> This is given to us by the square marking the right angle.

  • Segment BC ≅​ Segment DC (Side) -> This is given to us by the single markings on each line.

  • We also know that ∠ACB ≅ ∠ECD (Angle) because they are vertical angles and vertical angles are ALWAYS congruent.

​

​STOP! Example 3 inside foldable.

Therefore, this is Angle-Side-Angle since that is the order of congruence!

​

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • ∠C ≅​ ∠F (Angle) -> This is given to us by the single marking the right angle.

  • ∠CED ≅​ ∠FED (Angle) -> This is given to us by the double markings on each line.

  • We also know that Segment DE ≅ Segment DE (Side) because they are the same line.

​

​STOP! Example 4 inside foldable.

Therefore, this is Angle-Angle-Side since that is the order of congruence!

​

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent. All we know is the we have 2 parallel lines and line JL is the transversal.

  • ∠MJL ≅​ ∠KLJ (Angle) -> They are alternate interior angles (single markings)

  • We also know that Segment JL ≅ Segment JL (Side) because they are the same line.

  • ∠MLJ ≅​ ∠KJL (Angle) -> They are alternate interior angles (double markings)

​

​STOP! Example 5 inside foldable.

Therefore, this is Angle-Side-Angle since that is the order of congruence!

​