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justify triangle congruence Flashcards

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1
Q

What are the three main criteria for triangle congruence?

A

Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA).

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2
Q

True or False: If two triangles have two pairs of congruent sides and the included angle is congruent, the triangles are congruent.

A

True (this is SAS congruence).

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3
Q

Fill in the blank: The _____ criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

A

Angle-Side-Angle (ASA)

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4
Q

What does the SSS criterion stand for?

A

Side-Side-Side.

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5
Q

Which criterion would you use if you know two angles and a non-included side of two triangles are congruent?

A

Angle-Angle-Side (AAS).

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6
Q

True or False: Two triangles can be congruent if only one side is congruent.

A

False.

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7
Q

What is the definition of congruent triangles?

A

Triangles that have the same size and shape.

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8
Q

Which congruence criterion is applicable if two triangles have three pairs of congruent sides?

A

Side-Side-Side (SSS).

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9
Q

Fill in the blank: The _____ criterion is used when two sides and the angle opposite one of them are known to be congruent.

A

Side-Angle-Side (SAS)

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10
Q

What is the Angle-Angle-Angle (AAA) criterion?

A

It does not prove triangle congruence, only similarity.

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11
Q

True or False: The Hypotenuse-Leg (HL) theorem is a criterion for right triangles.

A

True.

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12
Q

What is the importance of the included angle in the SAS criterion?

A

It is the angle between the two sides being considered.

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13
Q

How many congruence criteria are there for triangles?

A

There are five main criteria: SSS, SAS, ASA, AAS, and HL.

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14
Q

What is the definition of the included side in triangle congruence?

A

The side that is between the two angles being considered.

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15
Q

Fill in the blank: The _____ theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent.

A

Hypotenuse-Leg (HL)

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16
Q

True or False: Two triangles can be congruent if they have two pairs of congruent angles and one pair of non-congruent sides.

A

False.

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17
Q

What is the relationship between congruent triangles and corresponding parts?

A

Corresponding parts of congruent triangles are congruent.

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18
Q

Which congruence criterion is invalid for proving triangle congruence?

A

Angle-Angle-Angle (AAA).

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19
Q

What can you conclude if two triangles are congruent by the SSS criterion?

A

All corresponding angles and sides are congruent.

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20
Q

True or False: The SAS criterion can be used if the angles are not included between the two sides.

A

False.

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21
Q

What does the AAS criterion stand for?

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A

Angle-Angle-Side.

22
Q

Fill in the blank: Two triangles are congruent if they have _____ pairs of corresponding sides that are congruent.

23
Q

What is the significance of congruence in geometry?

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A

It allows us to determine that two figures are identical in shape and size.

24
Q

True or False: If two triangles are similar, they must also be congruent.

25
What is the relationship between triangle congruence and symmetry?
Congruent triangles can demonstrate symmetry in geometric figures.
26
Fill in the blank: The _____ theorem is specifically for proving the congruence of right triangles.
Hypotenuse-Leg (HL)
27
What is the definition of triangle congruence?
Triangle congruence means that two triangles are identical in shape and size, having corresponding sides and angles equal.
28
Which postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent?
The Side-Angle-Side (SAS) Postulate.
29
True or False: The Angle-Side-Angle (ASA) Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
True.
30
Fill in the blank: The ________ Postulate asserts that two triangles are congruent if three sides of one triangle are equal to three sides of another triangle.
Side-Side-Side (SSS)
31
What does the Angle-Angle-Side (AAS) theorem state?
The AAS theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
32
Which congruence criterion is used when two triangles have two pairs of corresponding sides that are equal and the angle between those sides is also equal?
Side-Angle-Side (SAS) Congruence.
33
True or False: The Hypotenuse-Leg (HL) theorem is a specific case of the SAS postulate applicable only to right triangles.
True.
34
How can you prove that triangles are congruent using the SSS postulate?
By showing that all three corresponding sides of the triangles are equal in length.
35
What is necessary to prove triangle congruence using the ASA postulate?
You need to show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
36
Fill in the blank: The ________ theorem states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar but not necessarily congruent.
Angle-Angle (AA)
37
What is the significance of the corresponding parts of congruent triangles?
Corresponding parts of congruent triangles are equal, which can be used to prove further properties and theorems.
38
Which triangle congruence postulate can be used to prove the congruence of two right triangles if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle?
Hypotenuse-Leg (HL) Theorem.
39
True or False: The SSS postulate requires that all angles of the triangles be equal to establish congruence.
False.
40
What is the purpose of using triangle congruence in geometric proofs?
Triangle congruence is used to establish relationships between different figures and to prove further geometric properties.
41
Which postulate can be applied when proving the congruence of triangles that share a common side?
Side-Side-Side (SSS) Postulate.
42
Fill in the blank: The ________ theorem can be used to conclude that two triangles are congruent if two angles and a non-included side are known.
Angle-Angle-Side (AAS)
43
What criterion can be used to justify congruence if two triangles have one pair of equal sides and two pairs of equal angles?
Angle-Angle-Side (AAS) Criterion.
44
True or False: The congruence of triangles can be determined without any measurements, simply by comparing their shapes.
True.
45
What is the relationship between triangle similarity and triangle congruence?
All congruent triangles are similar, but not all similar triangles are congruent.
46
Which postulate is most commonly used in proofs involving congruent triangles?
Side-Angle-Side (SAS) Postulate.
47
Fill in the blank: The ________ theorem states that if two triangles have two sides equal and the angle opposite one of those sides is larger in one triangle, then that triangle is larger.
Triangle Inequality Theorem
48
What does it mean for triangles to be similar?
Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
49
True or False: You can prove triangle congruence using only angles.
False.
50
What is the necessary condition for two triangles to be congruent using the SAS postulate?
Two sides and the included angle of one triangle must be equal to two sides and the included angle of another triangle.

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