Review of Perpendicular and Angle Bisectors in Triangles

Triangles Review

Poll

How prepared to you feel for the assessment next class?

• Very! I got this

• Pretty good, need to go home and study some

• Definitely need to look over my notes and study

• I have absolutely no idea what I am doing and need to study and come to tutorials

​a segment that cuts an angle in half

​​Angle Bisector

​a segment from one vertex to the midpoint of the opposite side

​​Median

​a segment that is perpendicular to one side and cuts that side in half

​​Perpendicular Bisector

a segment from one vertex perpendicular to the side opposite the vertex

​​Altitude

Multiple Choice

Identify segment CD

• Median

• Perpendicular Bisector

• Angle Bisector

• Altitude

Multiple Choice

Identify segment CD

• Median

• Perpendicular Bisector

• Angle Bisector

• Altitude

Multiple Choice

Identify segment CD

• Median

• Perpendicular Bisector

• Angle Bisector

• Altitude

Multiple Choice

Identify segment CD

• Median

• Perpendicular Bisector

• Angle Bisector

• Altitude

Math Response

MP is a perpendicular bisector of NO. If NP = 33 and PO = 11x. Solve for x.

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

PQ is the altitude ΔMPN. What is the m∠MQP?

Type answer here

Correct Answer: 90

Deg^°

Rad

Math Response

SC is the median of ΔRSQ. If CQ = 119 and RC = 7x. Solve for x.

Type answer here

Correct Answer: 17

Deg^°

Rad

Math Response

LM is an angle bisector of ΔJLK.  If m∠1 = 72° and m∠2 = 6x° find x.

Type answer here

Correct Answer: 12

Deg^°

Rad

​Angle Notation Review

• find m< SRT means find the measure of angle SRT

• When an angle is written with three letters you are looking at the middle letter

Hotspot

Click on angle CBD

Hotspot

Click on angle DBA

• ​​Legs are congruent

• Base angles are congruent

​​Isosceles Triangles

• ​All sides are congruent

• All angles are congruent

​​Equilateral Triangle

Hotspot

Click on all the angles in the image

Dropdown

All angles in an equilateral triangle are equal to​ ​

Select answer

degrees.

​Angles vs Sides

• Angles in a triangle are different from the sides

• ANGLES and up to 180 degrees, sides can be any length

• ANGLES of an equilateral triangle are all equal to 60 degrees, sides are any length

Multiple Choice

How many degrees is angle A?

• 60

• 90

• 180

• Unknown

Multiple Choice

What is the length of side AB

• 60

• 90

• 180

• Unknown

Math Response

Solve for x.

Type answer here

Correct Answer: 6

Deg^°

Rad

Math Response

Solve for x.

Type answer here

Correct Answer: 16

Deg^°

Rad

​Can the Sides Make a Triangle

• Add the two smaller sides together

• If they are bigger than the third side it can be a triangle

• If they are smaller than the third side it can't be a triangle

Categorize

Options (6)

10, 17, 14

3, 4, 5

18, 13, 6

10, 5, 4

18, 12, 5

8, 9, 17

Can the three sides make a triangle?

Yes

No

Triangle Inequality Theorem

• Given two sides

• Subtract the two sides and make the answer less than x

• Add the two sides and make the answer less than x

Multiple Select

What can be the range of the third side of the triangle given the sides 14 and 26?

_____ < x < _____

• 40

• 14

• 12

• 26

• 32

• ​​C²<A²+B²

• ^{Acute is small so} C^{2 is smaller}

​​Acute

• ​​C²>A²+B²

• Obtuse is big so C² is bigger

​​Obtuse

• ​C²=A²+B²

• Right is just right so C² is equal

​​Right

Classifying triangles

• Use Pythagorean theorem

Categorize

Options (5)

8, 11, 6

8, 2, 9

12, 10, 15

9, 5, 10

3, 4, 5

Classify the following triangles

Obtuse

Acute

Right

Ordering Sides and Angles

• The largest angle is across from the longest side

• The smallest angle is across from the shortest side

Reorder

Put the sides in order from longest to shortest

• XY

• YZ

• XZ

1

2

3

• 1
• 2
• 3

Reorder

Put the angles in order from smallest to largest

• R

• P

• Q

1

2

3

• 1
• 2
• 3

​Remote Exterior Angle Theorem

• Exterior angle: angle on the outside of the triangle

• Remote interior angles: inside angles not adjacent to the exterior angle

• Theorem: The sum of the remote interior angles is equal to the exterior angle

Hotspot

What are the two remote interior angles?

Math Response

What is the value of x?

Type answer here

Correct Answer: 150

Deg^°

Rad

Math Response

What is the value of x?

Type answer here

Correct Answer: 77

Deg^°

Rad

​Triangle Congruence

• SSS- 3 corresponding sides are congruent

• SAS- 2 sides and included angle are congruent

• ASA- 2 angles and corresponding side are congruent

• AAS- 2 angles and non-included side are congruent

• HL- right triangle hypotenuses and 1 leg are congruent

Match

Determine by what theorem the triangles are congruent

HL

SAS

SSS

ASA

AAS

• HL

• SAS

• SSS

• ASA

• AAS

Dropdown

Triangle ABC is congruent to triangle​ ​

Select answer

​  

Poll

How prepared to you feel for the assessment next class?

• Very! I got this

• Pretty good, need to go home and study some

• Definitely need to look over my notes and study

• I have absolutely no idea what I am doing and need to study and come to tutorials