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6.4 Geometry Basics (Due 3/12/24)

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Last updated about 1 year ago
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Essential Question: What are the fundamental concepts of Geometry?

Learning Target: Students will be able to demonstrate understanding and give examples of the fundamental concepts of Geometry using their own examples.

Complete the entire assignment and show work for full credit.
Question 1
1.

What type of angle is formed by a straight line?

Question 2
2.

What is an angle between 90 and 180 degrees called?

Question 3
3.

What type of angle measures between 0 and 90 degrees?

Question 4
4.

Match the definition of the angle relationship with the angle relationships it describes...

Draggable itemarrow_right_altCorresponding Item
Two angles that are
adjacent and supplementary.
They form astraight line!
arrow_right_alt
Vertical angles
Any two angles whose sum is 180°
arrow_right_alt
Supplementary angles
Two angles that share a vertex and
a common side. They are next to each other
arrow_right_alt
Complementary angles
Two angles across from each other on
intersecting lines. They share a vertex and they are always congruent!
arrow_right_alt
Linear pairs
Any two angles whose sum is 90°
arrow_right_alt
Adjacent Angles
Question 5
5.

Select all the adjacent angles to ∠1

Question 6
6.

Select all the vertical angles to ∠1

Question 7
7.

Select all the adjacent angles to ∠7

Question 8
8.

Select all the supplemental angles to ∠1

Question 9
9.

Select all the vertical angles to ∠7

Question 10
10.
What is the value of x?_______

What kind of angles are these angles an examples of?_______

Question 11
11.
What is the value of x?_______


What kind of angles are these angles an examples of?_______

Question 12
12.
What are the values of x, y, and z?














x°=_______
y°=_______
z°=_______
Question 13
13.
What is the values of x, y, and z?


x°=_______
y°=_______
z°=_______

Part 2: Finding Measures of Angles with a Protractor

Question 14
14.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠AXB


Measure of the angle=_______

What kind of angle is it?=_______


Question 15
15.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠CXG


Measure of the angle=_______

What kind of angle is it?=_______


Question 16
16.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠DXA


Measure of the angle=_______

What kind of angle is it?=_______


Question 17
17.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠FXC


Measure of the angle=_______

What kind of angle is it?=_______


Question 18
18.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠AXG


Measure of the angle=_______

What kind of angle is it?=_______


Question 19
19.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠CXD


Measure of the angle=_______

What kind of angle is it?=_______


Question 20
20.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠BXF


Measure of the angle=_______

What kind of angle is it?=_______


Question 21
21.
Use the figure below to answer question. Find the measure of each angle, then classify it as acute, right, obtuse, or straight.

m∠EXA


Measure of the angle=_______

What kind of angle is it?=_______


Part 3 : Using Algebra

Question 22
22.

If m∠UVX= 76 and m∠XVW= 64, what is the measure of m∠UVW?


Question 23
23.

If m∠GHJ= 27 and m∠GHK= 87, what is the measure of m∠JHK?


Question 24
24.
Use the figure below to answer question. Let m∠MQP= 80.

m∠MQN=_______


m∠NQP=_______


Question 25
25.

If m∠PQT =109° and m∠SQR = (4x – 15)°, find the value of x.

Question 26
26.

If m∠PQT =109° what is the measure of m∠TQR?

Question 27
27.
Use the figure below to answer questions. Let m∠DAB= 136.

m∠CAB=_______


m∠CAD=_______


Question 28
28.

What is the correct order of steps to solve this problem?


  1. 6(24)-25=119; therefore the m∠SQR=119°
  2. Subtract 3x from both sides of the equation
  3. Add 25 to both sides of the equation
  4. Divide both sides of the equation by 3
  5. Make 3x+47 equal to 6x-25; because vertical angles are equal
  6. Substitute 24 for x into 6x-25 to find out what the m∠SQR equals
  7. x=24
Question 29
29.

What is the m∠SQR=?

Question 30
30.

If m∠DEG = (5x – 4)°, m∠GEF = (7x – 8)°, m∠DEH = (9y + 5)°, find the value of x.

Question 31
31.

Use the answer from the previous problem to find the measure of ∠GEF.

Question 32
32.

Use the answer from the previous problem.

If m∠DEG = (5x – 4)°, m∠GEF = (7x – 8)°, m∠DEH = (9y + 5)°, find the value of y.