Triangle Properties and Congruence Theorems

Triangle Properties and Congruence Theorems

by Donna Cook-Lujano

We will be reviewing the properties of Triangles, identifying components and features of special triangles, and will categorize certain triangles.

​Types of Triangles

Fill in the Blank

What type of triangle is this? Classify by the type of angle.

Multiple Choice

What type of triangle is this?

• Acute

• Equilateral

• Isosceles

• Scalene

Multiple Choice

What Type of Triangle is this?

• Right Angled triangle

• Equilateral triangle

• Isosceles triangle

• Scalene Triangle

• Acute Triangle

Multiple Choice

What Type of Triangle is this?

• Right Angled triangle

• Equilateral triangle

• Isosceles triangle

• Obtuse Triangle

• Acute Triangle

Multiple Choice

What Type of Triangle is this?

• Right Angled triangle

• Equilateral triangle

• Isosceles triangle

• Obtuse Triangle

• Acute Triangle

Multiple Select

Acute triangles are triangles with only acute angles inside.

Select all the acute triangles below:

Multiple Choice

What triangle has 1 obtuse angle and 2 acute angles?

• scalene triangle

• right triangle

• obtuse triangle

Multiple Choice

What triangle has one right angle and 2 acute angles?

• acute triangle

• right triangle

• obtuse triangle

Multiple Choice

What type of triangle is shown?

• Equilateral Triangle

• Scalene Triangle

• Isosceles Triangle

• Right Triangle

Multiple Choice

What type of triangle is this?

• Equilateral

• Isosceles

• Right

• Obtuse

Multiple Choice

Which type of triangle is pictured?

• Equilateral Triangle

• Right Isosceles Triangle

• Obtuse Isosceles Triangle

• Obtuse Equilateral Triangle

​Triangle Proof:

• ​We can prove triangles are congruent by SSS. This means we marked 3 sides.​

• ​We can prove triangles are congruent by SAS. This means we marked a Side, and Angle and a Side​

• ​We can prove triangles are congruent by ASA. This means we marked an Angle, a Side and then an Angle.

• We can prove triangles are congruent by AAS. This means we mark an angle, the next thing marked is an angle, and lastly the side is marked.

Multiple Choice

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

• SAS
• SSS
• ASA
• HL

Multiple Choice

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

• SSS
• ASA
• AAS
• SAS

Multiple Choice

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

• AAS
• SSS
• Not enough information given
• ASA

Multiple Choice

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

• AAS
• SSS
• SAS
• SSA

Multiple Choice

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

• SAS
• Not enough information
• SSS
• AAS

Multiple Choice

Which congruency statement can be written for the triangles pictured?

• $$\Delta ACB\cong\Delta ABD$$

• $$\Delta BAC\cong\Delta BAD$$

• $$\Delta CAB\cong\Delta DBA$$

• $$\Delta ADB\cong\Delta BCA$$

Multiple Choice

• Congruent by ASA
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

Multiple Choice

ΔABE ≅ Δ_____ by _____

• ΔCDE , ASA

• ΔEDC , AAS

• ΔCDE , AAS

• Cannot Be Determined

Multiple Choice

ΔQTR ≅ Δ_____ by _____

• ΔSTR , ASA

• ΔSTR , AAS

• ΔSRT , AAS

• Cannot Be Determined

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SAS
• ASA
• AAS
• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS

Multiple Choice

Identify the correct triangle congruence theorem.

• ASA

• AAS