Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

A Geometry > Proofs > Flashcards

Proofs Flashcards

1
Q

Given: Vertical Angles

A

Vertical Angles are Congruent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What should be done when given that segments bisect?

A

GIVEN: __ & __ bisects each other OR ___ bisects ____
1. Statement: ______ is the midpoint
1. Reason: A segment bisector meets at the midpoint
2. Statement: ______ congruent ________
2. A midpoint divides a segment into two congruent segments

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

How can supplementary angles be used in a proof? (4)

A

Two angles must have been proven congruent (X & Y)

  1. Statement: X & A are supplementary and Y & Z are supplementary
  2. Reason: Linear Pairs are Supplementary
  3. Statement: A = Z
  4. Supplements of congruent angles are congruent
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What should be done when given that angles bisect?

A

GIVEN: ___ bisects ____
Statement: ______ = _____
Reason: An angle bisector divides an angle into two congruent angles

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What must be done before proving two sides are congruent through addition and substractiction?

A

AC - BC = EC - DC
AB = ED

AC must be proven congruent to EC
BC must be proven congruent to DC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

How do you prove right angles?

A

Perpendicular Lines form right angles

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

How do you prove that the parts of two congruent sides are congruent?
Given: AB = CD, E mp of AB and F mp of CD

A

(Note: DO NOT NEED TO PROVE THAT THE PARTS OF THE SAME SIDEARE CONGRUENT)

  1. Statement: EB = 0.5 AB & FD = 0.5 CD
  2. Reason: Midpoint divides a segment in one half
  3. Statement: 0.5 AB = 0.5 CD
  4. Reason: Multiplication
  5. Statement: EB = FD
  6. Reason: Substitution
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

How can an Isosceles Triangles be used in Proofs? (2)

A
  1. In a triangle, angles opposite congruent sides are congruent
  2. In a triangle, sides opposite congruent angles are congruent
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

How do you prove parallel lines? (2)

A
  1. If 2 lines are cut by trans. such that (alt. int./corr./alt. ext.) angles are congruent, lines are parallel
  2. If 2 lines are cut by trans. such that cons. int. angles are supp., lines are parallel
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How do you use parallel lines in a proof? (2)

A
  1. If 2 parallel lines are cut by trans, then (alt. int./corr./alt. ext.) angles are congruent
  2. If 2 parallel lines are cut by trans, cons. int. angles are supplementary
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

How to prove two triangles are congruent?

A
  1. SAS
  2. ASA
  3. AAS
  4. HL
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How to prove two triangles are similar in proofs?

A

AA similarity Theorem
2 angles in one triangle are congruent to 2 angles in another triangle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

How do you utilize parts of congruent & similar triangles?

A
  1. Corresponding Parts of Congruent Triangles are Congruent
  2. Corresponding Parts of Similar Triangles are Similar
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How do you prove that two sides of similar triangles are in proportion and the products of the sides are in proportion?

A
  1. Prove Triangles are Similar through AA Sim. Theorem
  2. Corresponding Sides o Similar Triangles are in Proportion
  3. Products of Means = Products of Extremes
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What are three ways to prove an isosceles trapezoid?

A
  1. Must have at least one pair of congruent opposite sides
  2. Each pair of base angles are congruent
  3. Diagonals are congruent
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How can you prove a rectangle? (2)

A

Prove that is a parallelogram first, then use the following two properties to prove that the parallelogram is a rectangle:

  1. One right angle (rect. has 4 rt. angles)
  2. Diagonals are congruent (rect. is also an isoc. trapezoid)
14
Q

What are the five ways to prove a parallelogram?

A
  1. If both pairs of opposite sides are congruent , then the quad is a parallelogram
  2. If both pairs of opposite sides are parallel, then the quad is a parallelogram
  3. If both pairs of opposite angles are congruent, then the quad is a parallelogram
  4. If diagonals bisect each other, then the quad is a parallelogram (prove the mp)
  5. If ONE pair of opposite sides are both parallel & congruent, then the quad is a parallelogram
15
Q

What is something to keep in mind with when proving properties of a quadrilateral?

A

You may use all the properties that the quadrilateral posess except for the properties you are trying to prove.

16
Q

How can you prove a rhombus? (3)

A

Prove that is a parallelogram first, then use the following three properties to prove that the parallelogram is a rhombus:
1. Diagonals are perpendicular
2. Pair of consecutive sides are congruent
3. A diagonal bisects one set of angles

17
Q

How do you prove a square? (4)

A
  1. Prove it is a parallelogram
  2. Prove it is a rectangle
  3. Prove it is a rhombus
  4. A parallelogram has one property of a rhombus & rectangle, it’s a square
18
Q

How to prove a quad. to be rhombus thru perpendicular diagonals

A

(When they give you the rt. angle)
Statement - Diagonals (Segments name) are perpendicular
Reasoning - Perpendicular Lines form Right Angles

Statement - A quad is a rhombus
Reasoning - In kite/rhombus, diagonals are perpendicular to each other

19
Q

Reason for when you add to angles it forms the whole angle?

A

Angle Addition Postulate

A Geometry (21 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions