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Quizzes > Mathematics > Geometry

Geometry Chapter 1 & 2 Review Quiz: Test Your Skills!

Ready to ace your geometry chapter 1 review? Jump into the test and challenge yourself!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art geometry quiz scene on golden yellow background with shapes angles proofs ruler protractor

Use this Geometry Chapter 1 test to practice points, lines, angles, and basic proofs. You get instant scoring so you can spot gaps and review before the exam. When you're done, try the Unit 1 assessment or stretch yourself with the Chapter 9 quiz .

Which undefined term in geometry is represented by a location and has no size?
Point
Segment
Plane
Line
A point indicates a precise location in space without any dimension. It is one of the three undefined terms in Euclidean geometry, along with line and plane. All other geometric figures are defined using points. .
What term describes a straight one-dimensional figure extending infinitely in both directions?
Angle
Ray
Line
Segment
A line is a one-dimensional figure that extends infinitely in two directions and has no endpoints. It is an undefined term in geometry used to define segments and rays. Unlike a ray or segment, lines have no starting or ending points. .
Which undefined term describes a flat, two-dimensional surface extending infinitely in all directions?
Plane
Point
Ray
Line
A plane is a flat surface that extends infinitely in two dimensions and has no thickness. It is one of the three fundamental undefined terms in geometry. Any three noncollinear points determine a unique plane. .
What is the name of a part of a line consisting of two endpoints and all points between them?
Ray
Plane
Line
Segment
A segment consists of two endpoints and all points on the line between them. Its length can be measured using the Ruler Postulate. Segments differ from lines and rays because they are finite. .
According to the Ruler Postulate, if A is at 2 and B is at 7 on a number line, what is the length AB?
9
3
-5
5
The Ruler Postulate states that the distance between points is the absolute difference of their coordinates. Here, |7 - 2|=5. Negative lengths are not possible in geometry. .
On the coordinate plane, what is the distance between points (1,2) and (1,5)?
4
2
?10
3
Since both points share the same x-coordinate, the distance is |5 - 2| = 3. You can also apply the Distance Formula which reduces to a vertical difference here. This shows vertical segments are measured by y-coordinate differences. .
What is the midpoint of the segment with endpoints A(2,3) and B(4,7)?
(3,3)
(2,7)
(6,10)
(3,5)
The Midpoint Formula gives ((2+4)/2, (3+7)/2) = (3,5). This point is exactly halfway between A and B in both x- and y-directions. Midpoints partition segments into two equal lengths. .
How many degrees are in a straight angle?
180
45
90
360
A straight angle forms a straight line, which measures 180 degrees. It is twice the measure of a right angle (90°). Understanding angle measures is key to angle relationships later on. .
What do you call a ray that divides an angle into two congruent angles?
Altitude
Angle bisector
Perpendicular bisector
Median
An angle bisector splits an angle into two congruent angles. It is a fundamental construction in geometry, often made with compass and straightedge. This is different from a perpendicular bisector which relates to segments. .
According to the Angle Addition Postulate, if point B is interior to angle AOC, then m?AOB + m?BOC equals:
m?AOB × m?BOC
m?AOB - m?BOC
90°
m?AOC
The Angle Addition Postulate states that the measures of adjacent angles add to the measure of the larger angle they form. If B lies inside ?AOC, then the sum of ?AOB and ?BOC equals ?AOC. This is used in many geometric proofs. .
Two angles are complementary if their measures sum to:
90°
45°
180°
360°
Complementary angles have measures that add up to 90 degrees. Each angle in a complementary pair is called the complement of the other. This concept contrasts with supplementary angles. .
Two angles are supplementary if their measures sum to:
360°
90°
270°
180°
Supplementary angles have measures that add up to 180 degrees. A straight line creates a linear pair, which is always supplementary. This is fundamental for understanding angle relationships. .
What is formed by two adjacent supplementary angles?
Complementary angles
Vertical angles
Right angles
Linear pair
A linear pair consists of two adjacent angles whose non-common sides form a straight line, summing to 180°. They share a vertex and one side. Recognizing linear pairs helps solve for unknown angles. .
Vertical angles are always:
Supplementary
Adjacent
Congruent
Complementary
Vertical angles are the non-adjacent angles formed by two intersecting lines. They always have equal measures. This theorem is often used in proofs to establish angle congruence. .
What is the coordinate of the midpoint of a segment with endpoints (x?,y?) and (x?,y?)?
((x?+x?)/2, (y?+y?)/2)
(x??x?, y??y?)
((x?+y?)/2, (y?+x?)/2)
((x??x?)/2, (y??y?)/2)
The Midpoint Formula calculates the average of the x-coordinates and the average of the y-coordinates of the endpoints. This gives the exact center of the segment. It is widely used in analytic geometry. .
In what ratio does the point (4,3) divide the segment joining (2,1) and (6,5)?
2:3
4:1
1:1
3:2
Since (4,3) is the midpoint of (2,1) and (6,5), it divides the segment in a 1:1 ratio. Both horizontal and vertical differences are halved. This confirms equal partition. .
Given collinear points A, B, and C with AB = 5 and AC = 12, what is BC?
7
5
17
12
By the Segment Addition Postulate, if B is between A and C, then AB + BC = AC. So BC = 12 ? 5 = 7. This rule applies for any three collinear points. .
Using the Distance Formula, what is the distance between (?2,1) and (2,5)?
6
?20
8
4?2
Distance = ?[(2?(?2))² + (5?1)²] = ?[(4)² + (4)²] = ?(16+16) = ?32 = 4?2. The Distance Formula is derived from the Pythagorean Theorem. .
What is the midpoint of the segment with endpoints (?2,1) and (2,5)?
(-1,2)
(0,3)
(2,3)
(1,4)
Midpoint = ((?2+2)/2, (1+5)/2) = (0/2, 6/2) = (0,3). This splits the segment into two equal parts. The Midpoint Formula is an average of coordinates. .
Which point divides segment AB with A(1,2) and B(7,8) in a 1:2 ratio (internal)?
(3,4)
(4,5)
(7,2)
(5,6)
The section formula for internal division gives P = ((2·1 + 1·7)/(1+2), (2·2 + 1·8)/(1+2)) = (9/3, 12/3) = (3,4). This partitions AB in a 1:2 ratio. .
If m?1 = 2x + 10 and m?2 = 3x ? 5 and ?1 and ?2 are complementary, what is x?
15
18
12
17
Complementary angles sum to 90°, so (2x+10)+(3x?5)=90 ?5x+5=90 ?5x=85 ?x=17. Solving algebraic angle problems often uses this postulate. .
If two angles form a linear pair with m?A = 4x and m?B = 2x + 60, what is m?B?
60°
120°
100°
80°
Linear pairs sum to 180°, so 4x + (2x+60) = 180 ?6x+60=180 ?6x=120 ?x=20 ?m?B=2(20)+60=100°. This uses the definition of linear pairs. .
Which postulate states that through any three noncollinear points there is exactly one plane?
Plane Postulate
Ruler Postulate
Angle Addition Postulate
Segment Addition Postulate
The Plane Postulate asserts that any three points not on the same line determine a unique plane. This is fundamental to constructing and understanding geometric spaces. It complements the Line Postulate. .
Which postulate states that through any two points there is exactly one line?
Plane Postulate
Ruler Postulate
Line Postulate
Segment Addition Postulate
The Line Postulate (or Postulate 1) declares that any two distinct points lie on exactly one line. This is the basis for defining lines and segments in geometry. It contrasts with the Ruler Postulate, which involves distances. .
The Ruler Postulate allows us to establish a one-to-one correspondence between points on a line and which mathematical set?
Integers
Real numbers
Complex numbers
Rational numbers
The Ruler Postulate states that every point on a line corresponds to a real number and vice versa. This mapping enables measurement of segment lengths. It is essential for coordinate geometry. .
Which of the following is a theorem rather than a postulate?
The sum of measures of a linear pair is 180°
The measure of ?AOB + ?BOC equals ?AOC
Through any two points there exists exactly one line
Vertical angles are congruent
The congruence of vertical angles is established by proof and is known as the Vertical Angles Theorem. In contrast, the Line Postulate, Linear Pair sum, and Angle Addition Postulate are assumed without proof. Knowing which statements are theorems guides logical proofs. .
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Study Outcomes

  1. Classify Geometric Elements -

    Identify and distinguish between points, lines, planes, and the various types of angles to reinforce fundamental geometry concepts.

  2. Calculate Angle Measures -

    Compute and relate measures of complementary, supplementary, adjacent, and vertical angles to solve geometry problems accurately.

  3. Apply Postulates and Theorems -

    Use key geometry postulates and theorems to construct logical proofs and justify each step in problem solving.

  4. Analyze Segment Relationships -

    Apply segment addition and distance formulas to determine unknown lengths and verify relationships between points.

  5. Examine Parallel and Perpendicular Lines -

    Recognize angle relationships formed by transversals, and determine when lines are parallel or perpendicular in a plane.

  6. Interpret Instant Feedback -

    Use scored results and detailed explanations to pinpoint errors, correct misconceptions, and strengthen your problem-solving strategies.

Cheat Sheet

  1. Fundamental Geometric Definitions -

    Master the precise terms point, line, plane, segment, and ray as outlined in Euclid's postulates, and practice notation like segment AB and ray AB. Remember that points have no dimension, lines extend infinitely in both directions, and planes are flat two-dimensional surfaces.

  2. Segment Addition and Midpoint Postulates -

    Use the Segment Addition Postulate (if A, B, C are collinear, then AB + BC = AC) to solve for unknown lengths; for example, if AB = 3 and BC = x, and AC = 8 then x = 5. Apply the Midpoint Definition to recognize that a midpoint divides a segment into two congruent parts, so AM = MB when M is the midpoint of AB.

  3. Angle Types and Relationships -

    Distinguish complementary (sum = 90°), supplementary (sum = 180°), vertical (opposite and congruent), and linear pair (adjacent and supplementary) angles, and use a mnemonic like "complements complete" to recall 90°. Practice labeling angles with notation such as ∠ABC and use the Angle Addition Postulate (if point D is interior to ∠ABC, then ∠ABD + ∠DBC = ∠ABC).

  4. Parallel Lines and Transversal Theorems -

    Identify corresponding, alternate interior, and alternate exterior angles formed when parallel lines are cut by a transversal, using the "Z-shape" trick for alternate interior angles and "F-shape" for corresponding angles that are congruent. Apply these theorems to find missing angle measures, such as knowing alternate interior angles are equal when lines are parallel.

  5. Triangle Sum and Exterior Angle Theorems -

    Recall that the sum of interior angles in any triangle is 180° (∠A + ∠B + ∠C = 180°) and that an exterior angle equals the sum of its two remote interior angles, so ∠ACD = ∠A + ∠B when CD is an extension of BC. Use these properties to solve for angles in complex diagrams and verify results quickly.

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