Definition of Congruency for Triangles: CCSS.Math.Content.HSG-CO.B.7 - Common Core: High School - Geometry
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What must be true if 
has had a rigid motion applied to it to result in 
?
What must be true if
Recall that a rigid motion preserves the distance from points within a shape in the plane. Therefore, if has had a rigid motion applied to it to result in that means that all corresponding sides and angles of these two triangle are congruent.
Therefore, the statement "both corresponding angles and sides are congruent" is the correct solution to this particular question.
Recall that a rigid motion preserves the distance from points within a shape in the plane. Therefore, if
Therefore, the statement "both corresponding angles and sides are congruent" is the correct solution to this particular question.
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Determine whether the statement is true or false:
Two triangles that are congruent have corresponding points that are separated five spaces. These two triangles describe a rigid motion.
Determine whether the statement is true or false:
Two triangles that are congruent have corresponding points that are separated five spaces. These two triangles describe a rigid motion.
Recall that a rigid motion preserves the distance from points within a shape in the plane. Since the statement clearly states that the two triangles are congruent, that means that the distances between the points within the shape are preserved. Also, since the corresponding points between the two triangles are separated by five spaces this is describing a translation which when combined with the preserved shape, describes a rigid motion. Therefore, the statement is true.
Recall that a rigid motion preserves the distance from points within a shape in the plane. Since the statement clearly states that the two triangles are congruent, that means that the distances between the points within the shape are preserved. Also, since the corresponding points between the two triangles are separated by five spaces this is describing a translation which when combined with the preserved shape, describes a rigid motion. Therefore, the statement is true.
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When a rigid motion is done onto A, C is the resulting image. Are triangles A and C congruent?
When a rigid motion is done onto A, C is the resulting image. Are triangles A and C congruent?
Recall that a rigid motion preserves the distance from points within a shape in the plane. It appears that the rigid motion was a rotation. The third angle can be identified by subtracting the two known angles from 180 degrees.
Triangle A:
Triangle C:
Since the side between two angles on triangle C is congruent to the side between those same two angles on triangle A, the two triangles are congruent.
Recall that a rigid motion preserves the distance from points within a shape in the plane. It appears that the rigid motion was a rotation. The third angle can be identified by subtracting the two known angles from 180 degrees.
Triangle A:
Triangle C:
Since the side between two angles on triangle C is congruent to the side between those same two angles on triangle A, the two triangles are congruent.
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Determine whether the statement is true or false.
An equilateral triangle 
is rotated counter clockwise and transformed into an isosceles triangle 
. 
is congruent to 
.
Determine whether the statement is true or false.
An equilateral triangle
To determine whether this statement is true or false, first recall what it means to be "congruent". Congruent means equal or in more mathematical terms, both corresponding angles and sides of the two triangles are congruent.
The statement says that 
is an equilateral triangle which means all sides and angles are the same. After the triangle goes through a transformation, it becomes an isosceles triangle. To be isosceles means that two of the sides and angles of the triangle are the same. Since, not all of the angles are the same in 
it is not congruent to 
.
Therefore, the statement, "
is congruent to 
." is false.
To determine whether this statement is true or false, first recall what it means to be "congruent". Congruent means equal or in more mathematical terms, both corresponding angles and sides of the two triangles are congruent.
The statement says that
Therefore, the statement, "
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Which of the following geometric theorems cannot prove triangle congruency?
Which of the following geometric theorems cannot prove triangle congruency?
To determine which theorem cannot prove triangle congruency, first recall what it means to be "congruent". Congruent means equal or in more mathematical terms, both corresponding angles and sides of the two triangles are congruent.
There are five theorems used in geometry to prove whether two triangles are congruent.
1. Side, Side, Side
2. Side, Angle, Side
3. Angle, Side, Angle
4. Angle, Angle, Side
5, Hypotenuse and One Leg from Right Triangle
Of the answers below, Angle, Angle, Angle (AAA) is not among one of the theorems to prove triangle congruency. The reason AAA does not prove triangle congruency because two triangles can have the same angles but have different side lengths thus, the triangles would not be congruent.
To determine which theorem cannot prove triangle congruency, first recall what it means to be "congruent". Congruent means equal or in more mathematical terms, both corresponding angles and sides of the two triangles are congruent.
There are five theorems used in geometry to prove whether two triangles are congruent.
1. Side, Side, Side
2. Side, Angle, Side
3. Angle, Side, Angle
4. Angle, Angle, Side
5, Hypotenuse and One Leg from Right Triangle
Of the answers below, Angle, Angle, Angle (AAA) is not among one of the theorems to prove triangle congruency. The reason AAA does not prove triangle congruency because two triangles can have the same angles but have different side lengths thus, the triangles would not be congruent.
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Which theorem can be used to prove triangle congruency between triangle A and C?
Which theorem can be used to prove triangle congruency between triangle A and C?
For this particular problem there are two geometric theorems that can prove that the triangles are similar.
The geometric theorems that could be used:
1. Angle, Side, Angle (ASA)
2. Angle, Angle, Side (AAS)
For triangle C the AAS is the most evident to use. Since ASA is not an option in the answer selections, AAS is the correct answer.
For this particular problem there are two geometric theorems that can prove that the triangles are similar.
The geometric theorems that could be used:
1. Angle, Side, Angle (ASA)
2. Angle, Angle, Side (AAS)
For triangle C the AAS is the most evident to use. Since ASA is not an option in the answer selections, AAS is the correct answer.
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Which theorem can be used to prove triangle congruency between triangle A and C?
Which theorem can be used to prove triangle congruency between triangle A and C?
For this particular problem there are two geometric theorems that can prove that the triangles are similar.
The geometric theorems that could be used:
1. Angle, Side, Angle (ASA)
2. Angle, Angle, Side (AAS)
For triangle C the AAS is the most evident to use. Since AAS is not an option in the answer selections, ASA is the correct answer.
For this particular problem there are two geometric theorems that can prove that the triangles are similar.
The geometric theorems that could be used:
1. Angle, Side, Angle (ASA)
2. Angle, Angle, Side (AAS)
For triangle C the AAS is the most evident to use. Since AAS is not an option in the answer selections, ASA is the correct answer.
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Which theorem can be used to prove triangle congruency between triangle A and B?
Which theorem can be used to prove triangle congruency between triangle A and B?
For this particular problem there are two geometric theorems that could potentially be used to prove that the triangles are similar.
The geometric theorems that could be used:
1. Hypotenuse and One Leg of a Right Triangle (HL)
2. Side, Side, Side (SSS)
To use SSS or HL, the Pythagorean theorem will need to be used to calculate the missing side.
For these triangles the HL is the most evident to use and since SSS is not an option in the answer selections, HL is the correct answer.
For this particular problem there are two geometric theorems that could potentially be used to prove that the triangles are similar.
The geometric theorems that could be used:
1. Hypotenuse and One Leg of a Right Triangle (HL)
2. Side, Side, Side (SSS)
To use SSS or HL, the Pythagorean theorem will need to be used to calculate the missing side.
For these triangles the HL is the most evident to use and since SSS is not an option in the answer selections, HL is the correct answer.
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Which theorem can be used to prove triangle congruency between triangle A and B?
Which theorem can be used to prove triangle congruency between triangle A and B?
For this particular problem there are two geometric theorems that could potentially be used to prove that the triangles are similar.
The geometric theorems that could be used:
1. Hypotenuse and One Leg of a Right Triangle (HL)
2. Side, Side, Side (SSS)
To use SSS or HL, the Pythagorean theorem will need to be used to calculate the missing side.
For these triangles the HL is the most evident to use but is not an option in the answer selections, therefore, SSS is the correct answer.
For this particular problem there are two geometric theorems that could potentially be used to prove that the triangles are similar.
The geometric theorems that could be used:
1. Hypotenuse and One Leg of a Right Triangle (HL)
2. Side, Side, Side (SSS)
To use SSS or HL, the Pythagorean theorem will need to be used to calculate the missing side.
For these triangles the HL is the most evident to use but is not an option in the answer selections, therefore, SSS is the correct answer.
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Identify the missing term in the statement.
The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known.
Identify the missing term in the statement.
The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known.
The statement, "The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known." is describing the geometric theorem known as the Hypotenuse and One Leg theorem. When abbreviated this is seen as, HL.
Therefore, the missing term is, Hypotenuse and One Leg (HL)
The statement, "The __________ geometric theorem deals with proving congruency among right triangles; specifically when the length of one leg and the length of the hypotenuse are known." is describing the geometric theorem known as the Hypotenuse and One Leg theorem. When abbreviated this is seen as, HL.
Therefore, the missing term is, Hypotenuse and One Leg (HL)
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Identify the missing term in the statement.
The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent.
Identify the missing term in the statement.
The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent.
The statement, "The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent." is describing the geometric theorem known as the Side, Side, Side theorem. When abbreviated this is seen as, SSS.
Therefore, the missing term is, Side, Side, Side (SSS).
The statement, "The __________ geometric theorem can be used to identify whether triangles that each have three known side lengths are congruent." is describing the geometric theorem known as the Side, Side, Side theorem. When abbreviated this is seen as, SSS.
Therefore, the missing term is, Side, Side, Side (SSS).
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Identify the missing term in the statement.
When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________.
Identify the missing term in the statement.
When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________.
The statement, "When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________. " is describing the geometric theorem known as the Angle, Side, Angle theorem. When abbreviated this is seen as, ASA.
Therefore, the missing term is, Angle, Side, Angle (ASA).
The statement, "When two triangles have two known angles and a known side length that is in between the angles, the geometric theorem that can be used to prove congruency is known as __________. " is describing the geometric theorem known as the Angle, Side, Angle theorem. When abbreviated this is seen as, ASA.
Therefore, the missing term is, Angle, Side, Angle (ASA).
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