Segment Addition Postulate

If points A, B, and C are on the same line with B between A and C, then AB + BC =AC.

Angle Addition Postulate

If point D is in the interior of <ABC, then m∠ABD + m∠DBC = m∠ABC.

Segments that have the same length.

Angles that have the same measure are congruent angles.

Reflexive Property of Congruence

(AB) ̅≅(AB) ̅ . ∠A ≅∠A

Symmetric Property of Congruence

If (AB) ̅≅CD , then (CD) ̅≅(AB) ̅ . If ∠A ≅∠B then ∠B ≅∠A

Transitive Property of Congruence

If (𝐴𝐵) ̅≅(CD) ̅ and (CD) ̅≅(EF) ̅" then " (𝐴𝐵) ̅≅(EF) ̅. If ∠𝐴 ≅∠𝐵 and ∠B ≅∠C then ∠A ≅∠C.

Step 1: To copy (AB) ̅, first use a straightedge to draw line l. Mark point C on line l. Step 2: Place the compass point at A, and open the compass to length AB. Step 3: Using the same setting place the compass point at C and draw an arc through line l. Mark point D at the intersection.

Step 1: Mark a point X. Use a straightedge to draw a ray with endpoint X. Step 2: Place the compass point at A. Draw an arc that intersects both rays of ÐA. Label the points of intersection B and C. Step 3: Without changing the setting, place the compass point at X and draw an arc intersecting the ray. Mark the point Y at the intersection. Step 4: Place the compass point at C, and open the compass the distance between B and C. Step 5: Without changing the setting, place the compass at Y and draw an arc. Label the point Z where the two arcs intersect. Use a straightedge to draw →┬XZ

Perpendicular ( I ) bisector

Step 1: With a setting greater than 1/2 AB, place the compass point at A. Draw arc above and below (AB) ̅. Step 2: With the same setting, place the compass point at b. Draw arcs above and below (AB) ̅. Step 3: Label the points of intersection of the arcs E & F. Use a straightedge to draw .(EF)

Step 1: Place the compass point at A. Draw an arc intersecting both rays of ÐA. Label the points of intersection B and C. Step 2: Place the compass point at B. draw an arc in the interior of ÐA. With the same setting, place the compass point at C and draw an arc intersecting the arc drawn from B. Step 3: Label the point of intersection of the two arcs D. Use a straightedge to draw AD.

an average that favors numbers, or points, with greater weight

determine weighted averages

Step 1: Find the weights at the given points. Do this by setting up an algebraic equation. Step 2: solve the equation to get the ratio for the weights. Step 3: Use the ratio to find the weighted average by multiplying with the ratio and the original given points.

Step 1: Find the horizontal distance by multiplying the weight by the absolute value of the given x-coordinates. Step 2: Find the vertical distance by multiplying the weight by the absolute value of the given y-coordinates. Step 3: Add the horizontal distance to the x-value of the first point to get the new x-coordinate. Step 4: Add the vertical distance to the y-value of the first point to get the new y-coordinate.

An if-then statement that relates a hypothesis, the part that follows if, to a conclusion, the part that follows then.

The truth value of a statement is “true” (T) or “false” (F) according to whether the statement is true or false, respectively.

a table that lists all the possible combinations of truth values for two or more statements.

An unproven statement or rule that is based on inductive reasoning.

An example that shows a statement or conjecture is false.

The converse reverses the hypothesis and conclusion of a conditional.

has the opposite meaning of the original statement

is obtained by negating both the hypothesis and the conclusion of a conditional

is obtained by negating and reversing the hypothesis and the conclusion of a conditional.

biconditional statement

is the combination of a conditional statement ,p→q, and its converse, q→p. A biconditional contains the words “if and only if.”

vertical angles theorem

If two angles are vertical angles, then the angles are congruent.

congruent supplements theorem

If two angles are supplementary to congruent angles or to the same angle), then they are congruent

congruent complements theorem

If two angles are complementary to congruent angles (or to the same angle), then they are congruent.

If two angles are congruent and supplementary, then each is a right angle.

The sum of the measures of a linear pair is 180.

Geometry Chapter 1 Flash Cards Flashcards

Student preview

38 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Point

Back

A location that has no shape or size.

2.

FLASHCARD QUESTION

Front

Line

Back

Made up of points and has no thickness or width.

3.

FLASHCARD QUESTION

Front

Plane

Back

A flat surface made up of points and extends indefinitely in all directions.

4.

FLASHCARD QUESTION

Front

Segment

Back

The part of a line that consists of two endpoints and all points between them.

5.

FLASHCARD QUESTION

Front

Ray

Back

Part of a line that consists of one endpoint and extends indefinitely in the other direction.

6.

FLASHCARD QUESTION

Front

Angle

Back

Formed by two rays with the same endpoint. Each ray is the side of the angle, and the common endpoint is the vertex of the angle.

7.

FLASHCARD QUESTION

Front

Collinear

Back

on the same line .

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