Common Core: High School - Geometry : Congruence

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #7 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

Which theorem can be used to prove triangle congruency between triangle A and B?

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Possible Answers:

AAS

AAA

SAS

ASA

SSS

Correct answer:

SSS

Explanation:

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.

Example Question #8 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

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.

Possible Answers:

Side, Angle, Side

Angle, Angle, Side (AAS)

Hypotenuse and One Leg (HL)

Angle, Angle, Angle (AAA)

Side, Side, Side (SSS)

Correct answer:

Hypotenuse and One Leg (HL)

Explanation:

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)

Example Question #11 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

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.

Possible Answers:

Side, Side, Side (SSS)

Side, Angle, Side (SAS)

Angle, Side, Angle (ASA)

Angle, Angle, Side (AAS)

Hypotenuse and One Leg (HL)

Correct answer:

Side, Side, Side (SSS)

Explanation:

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).

Example Question #12 : Definition Of Congruency For Triangles: Ccss.Math.Content.Hsg Co.B.7

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 __________

Possible Answers:

Side, Side, Side (SSS)

Angle, Angle, Angle (AAA)

Angle, Angle, Side (AAS)

Angle, Side, Angle (ASA)

Side, Angle, Side (SAS)

Correct answer:

Angle, Side, Angle (ASA)

Explanation:

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).

Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is 

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is 

Now we simply substitute the answer we just got for .

So the answer is .

Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of 

The complement is 

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is 

Now we simply substitute the answer we just got for .

So the answer is .

Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is 

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is 

Now we simply substitute the answer we just got for .

So the answer is 

Example Question #81 : High School: Geometry

What is the supplement of the complement of ?

 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of .

The complement is 

Since we are given an angle of  we can substitute it for , and solve for.

Now since we need to find the supplement of the answer, we just got.

The supplement is 

Now we simply substitute the answer we just got for .

So the answer is 

Example Question #4 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of ?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of 

The complement is 

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is 

Now we simply substitute the answer we just got for .

So the answer is 

Example Question #82 : High School: Geometry

What is the supplement of the complement of ?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of 

The complement is

Since we are given an angle of  we can substitute it for , and solve for .

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for 

So the answer is 

All Common Core: High School - Geometry Resources

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