Intro to Geometry Overview

​Introduction to Geometry

Survey of Math

Line Segments

Math Response

If $$PQ=9$$ and $$RQ=28$$ , find PR.

Type answer here

Correct Answer: 37

Deg^°

Rad

Math Response

If $$QR=17$$ and $$PR=21$$ , find PQ.

Type answer here

Correct Answer: 4

Deg^°

Rad

Math Response

If $$PQ=11$$ and $$PR=54$$ , find QR.

Type answer here

Correct Answer: 43

Deg^°

Rad

Line Segments

All segments can be divided into 2 congruent segments by a point called the midpoint. A line, ray, or segment that intersects a segment at its midpoint is said to bisects the segment and is called the segment bisector.

Multiple Choice

If Q is the midpoint of PR, which of the following equations would be used to solve for x?

• $$7x+4x=-16+2$$

• $$7x-16=4x+2$$

• $$2+7x=-16+4x$$

Angles

An angle is formed by two rays with a common endpoint called a vertex. The rays are called the sides. Name an angle using 3 letters and the middle letter MUST always represent the vertex (unless there is only one angle located at the vertex). When referring to the measure of an angle, use a lowercase m.

Multiple Select

Select ALL the possible options of the measure of this angle.

• $$m\angle ABC=60\degree$$

• $$m\angle CBA=60\degree$$

• $$m\angle B=60\degree$$

• $$m\angle A=60\degree$$

• $$m\angle C=60\degree$$

Categorize

Options (8)

measures less than 90

measures exactly 90

measures greater than 90

measures exactly 180

Match the types of angles with their respective example and definition.

Acute

Right

Obtuse

Straight

Angles

Math Response

If $$m\angle ABD=48\degree$$ and $$m\angle DBC=78\degree$$ , find $$m\angle ABC$$

Type answer here

Correct Answer: 126

Deg^°

Rad

Math Response

If $$m\angle ABC=119\degree$$ and $$m\angle DBC=74\degree$$ , find $$m\angle ABD$$

Type answer here

Correct Answer: 45

Deg^°

Rad

​Types of Angle Pairs

​Relationship	Definition​
Vertical Angles​	​When 2 lines intersect at a point they are the angles that are equal to each other.
Complementary​	​Two angles with measures that add up to 90
Supplementary	​Two angles with measures that add up to 180 *A linear pair are 2 angles that form a line

*Draw your own examples in your notes packet

Match

Name a pair of adjacent angles, a pair of

complementary angles, and a pair of supplementary angles.

• Adjacent Angles

• Complementary Angles

• Supplumentary Angles

• $$\angle DAC\ \&\ \angle BAC$$

• $$\angle BAC\ \&\ \angle RST$$

• $$\angle DAC\ \&\ \angle RST$$

Categorize

Options (12)

$$\angle1\ \&\ \angle4$$  

$$\angle4\ \&\ \angle3$$  

$$\angle3\ \&\ \angle2$$  

$$\angle2\ \&\ \angle1$$  

$$\angle8\ \&\ \angle7$$  

$$\angle7\ \&\ \angle6$$  

$$\angle6\ \&\ \angle5$$  

$$\angle5\ \&\ \angle8$$  

$$\angle1\ \&\ \angle3$$  

$$\angle2\ \&\ \angle4$$  

$$\angle5\ \&\ \angle7$$  

$$\angle6\ \&\ \angle8$$  

Name all the linear pairs and vertical angles in the figure.

Linear Pairs

Vertical Angles

Dropdown

​ Complete the following sentences.

a. ∠1 is a complement of ∠2. If the m∠1 = 49°, then the m∠2 is ​

Select answer

º.

b. ∠3 is a supplement of ∠4. If the m∠3 = 119°, then the m∠4 is ​

Select answer

º.

c. ∠5 and ∠6 and vertical angles. If the m∠5 = 33°, then the m∠6 is ​

Select answer

º.

d. ∠B and ∠A are a linear pair. If the m∠A = 65.2°, then the m∠B is ​

Select answer

º.

Triangles

A triangle is a polygon with three (3) sides and three (3) angles.

We can classify triangles by using either the angles and/or the sides.

​Classify by Angles

​Classify by Sides

Match

Classify the following triangles by angles and by sides. (You may have to solve for the value of x in some of the triangles.)

right

isosceles

acute

scalene

obtuse

scalene

acute

scalene

equiangluar

equilateral

• right

  isosceles

• acute

  scalene

• obtuse

  scalene

• acute

  scalene

• equiangluar

  equilateral

Math Response

Solve for the value of x. Type only the number!

Type answer here

Correct Answer: 27

Deg^°

Rad

Multiple Select

Write an equation to solve for the value of x.

HINT: There may be more than one answer!

• $$3x-1=31$$

• $$3x-1=59$$

• $$\left(3x-1\right)+31=180$$

• $$\left(3x-1\right)+31=90$$

• $$\left(3x-1\right)+31+90=180$$