Lesson 2.5: Triangle Congruence Theorems (Day 1)

Lesson 2.5: Triangle Congruence Theorems (Day 1)

By Ms. Wiley

Multiple Choice

If ∆CAB≅∆FED , then $$\angle C\cong\angle F$$  

• True

• False

Multiple Choice

If ∆LMK ≅ ∆LMT, then ∠K ≅ ____ 

• $$L$$  

• $$\angle L$$  

• $$\angle T$$  

• T

Multiple Choice

If $$\Delta MAN\cong\Delta BOY$$ , which of the following statements are true?

• $$\overline{MA}\cong\overline{BO}$$  

• $$\overline{AN}\cong\overline{BY}$$  

• $$\overline{BO}\cong\overline{NA}$$  

• $$\overline{MN}\cong\overline{BO}$$  

Side-Side-Side Theorem

Multiple Select

Which set of figures cannot be proved congruent using Side-Side-Side Congruence Theorem.

Multiple Choice

How are the triangles congruent?

• SAS
• SSS
• HL
• ASA

Multiple Choice

How are the triangles congruent?

• SAS
• SSS
• ASA
• HL

​Two sides are congruent

and

The angles between the sides are congruent

​

Remember.......

Vertical angles are congruent​ so when

you see them​ mark them as congruent.

​SAS Review

Multiple Choice

Does SAS prove the triangles are congruent?

• Yes

• No

Multiple Choice

Does SAS work to prove the triangles are congruent?

• No, there are no congruent angles

• Yes, two sides are congruent and the included angle is congruent because they are vertical angles

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS

• SAS

• None

Multiple Choice

How are the triangles congruent?

• SAS

• SSS

• Not congruent

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS

• SAS

• Not congruent

Multiple Choice

When can we use the HL Congruence Theorem?

• Right Triangles
• Isosceles Triangles
• When we have a reflexive side
• SSA

Hyptenuse-Leg Theorem

Multiple Choice

How are the triangles congruent?

• HL
• SSS
• SAS
• AAS

Multiple Choice

How are the triangles congruent?

• SAS
• ASA
• HL
• SSS

Unit 2 Review (so far...)

We will be having our Unit 2 Test is next Thursday (possibly Friday). These next slides take you through a review of what we've talked about so far!

Multiple Choice

What is the sum of all of the interior angles of a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Two Ways to Classify Triangles

● By their angles

● By their sides

Multiple Select

What are two ways to classify triangles? SELECT BOTH!

• Angles

• Height

• Sides

• Orientation

Multiple Choice

Name of a triangle with 2 congruent sides?

• Equilateral

  Triangle

• Isosceles

  Triangle

• Scalene

  Triangle

Multiple Choice

Name of a triangle with 3 congruent sides?

• Equilateral

  Triangle

• Isosceles

  Triangle

• Scalene

  Triangle

Multiple Choice

Name of a triangle with no congruent sides?

• Equilateral

  Triangle

• Isosceles

  Triangle

• Scalene

  Triangle

Multiple Choice

Name of a triangle with 3 congruent angle?

• Equiangular

  Triangle

• Right

  Triangle

• Acute

  Triangle

• Obtuse

  Triangle

Multiple Choice

Name of a triangle with 1 right angle?

• Equiangular

  Triangle

• Right

  Triangle

• Acute

  Triangle

• Obtuse

  Triangle

Multiple Choice

Name of a triangle with 1 obtuse angle?

• Equiangular

  Triangle

• Right

  Triangle

• Acute

  Triangle

• Obtuse

  Triangle

Multiple Choice

Name of a triangle with 1 acute angle?

• Equiangular

  Triangle

• Right

  Triangle

• Acute

  Triangle

• Obtuse

  Triangle

Important Note:

● Triangles can be classified by sides and angles at the same time.



Examples:

Multiple Select

Select the TWO classifications for the triangle

• Equilateral

• Scalene

• Isosceles

• Equiangular

• Obtuse

Multiple Select

Select the TWO classifications for the triangle

• Isosceles

• Scalene

• Right

• Obtuse

• Acute

Sum of the interior angles of a triangle

• The angles inside a triangle ALWAYS add up to be 180 degrees

• It does not matter what type of triangle it is, the angles always add up to be 180 degrees

Multiple Choice

Find the measure of the missing angle.

• 90^o

• 10⁰

• 130^o

• 50^o

Multiple Choice

Find the measure of the missing angle.

• 47

• 57

• 53

• 133

Multiple Choice

Solve for x.

• 28
• 12
• 10
• 2

Multiple Choice

Find the measure of angle A.

• 75^o
• 60^o
• 30^o
• 38^o

Finding x

Remember the sum of the remote interior angles equals the exterior angle.

So........

63 + 86 = x

149 ^o = x

Finding x when it is a interior angle!

• The sum of the remote interior angles equals the exterior angle.

• x + 40 = 100

• -40 from both sides

• x = 60^o

Multiple Choice

Which of the following terms best describes Angle d?

• Remote interior angle

• Corresponding angle

• Exterior angle

• Interior angle

Multiple Choice

Find the measure of angle x. Be careful! They did NOT give you two remote interior angles.

• 138

• 96

• 93

• 87

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Which of the following angles can you add together to equal angle d? 

• Angle a and Angle b
• Angle b and Angle c
• Angle a and Angle c
• Angle a and Angle b and Angle c

Multiple Choice

Choose a correct equation to find x.

• 4x - 2 + 12x + 1 = 75

• 4x - 2 + 75 = 12x + 1

• 4x - 2 + 75 + 12x + 1 = 180

• 4x - 2 - 75

Angles and Sides

• The smallest angle will be opposite the  shortest side

• While the largest angle will be opposite the longest side.

• A side is congruent to another side if it has an equal length.

Multiple Choice

Which side of the triangle should be the longest?

• A

• B

• C

Multiple Choice

What is the smallest angle?

• K
• L
• M

Multiple Choice

What is the biggest side?

• LM
• MN
• LN

Triangle Inequality

To form a triangle, the sum of any two side lengths MUST be GREATER THAN the last side length.

a + b > c

b + c > a

a + c > b

Triangle Inequality

Not every group of three segments can be used to form a triangle. The lengths of the segments must fit a certain relationship.

Multiple Choice

Will these side lengths form a triangle?

12, 2, 18

• yes

• no

Multiple Choice

Will these three sides form a triangle?

26, 5, 24

• yes

• no

Multiple Choice

Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60

• 28, 30, 58

• 13, 20, 27

• 2, 4, 5

Multiple Select

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

• 4, 4, 4

• 5, 5, 10

• 3, 6, 9

• 5, 7, 11

• 13, 5, 6

Multiple Choice

Which set of side lengths could NOT be used to form a triangle?

• 2 cm, 6 cm, 7 cm

• 7 cm, 15 cm, 8 cm

• 5 cm, 5 cm, 5 cm

• 8 cm, 9 cm, 6 cm

Multiple Select

If a triangle has shorter side lengths of 12 cm and 14 cm, which of the following could not be the 3rd side length?

Select all that apply.

• 27 cm

• 23 cm

• 42 cm

• 30 cm