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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 #71 : Congruence

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, Angle, Side (SAS)

Angle, Side, Angle (ASA)

Angle, Angle, Side (AAS)

Hypotenuse and One Leg (HL)

Side, Side, Side (SSS)

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).

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Example Question #72 : Congruence

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:

Angle, Angle, Angle (AAA)

Angle, Angle, Side (AAS)

Angle, Side, Angle (ASA)

Side, Side, Side (SSS)

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).

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

What is the supplement of the complement of $50^{\circ}$ ?

Possible Answers:

$50^{\circ}$

$100^{\circ}$

$40^{\circ}$

$130^{\circ}$

$140^{\circ}$

Correct answer:

$140^{\circ}$

Explanation:

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

We need to first find the complement of $50^{\circ}$ .

The complement is

90 = x + y

Since we are given an angle of $50^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 50 \\y = 40$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for $\uptext{x}$ .

$\\180 = y + 40 \\y = 140$

So the answer is $140^{\circ}$ .

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Example Question #73 : Congruence

What is the supplement of the complement of $81^{\circ}$ ?

Possible Answers:

$171^{\circ}$

$162^{\circ}$

$9^{\circ}$

$99^{\circ}$

$81^{\circ}$

Correct answer:

$171^{\circ}$

Explanation:

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

We need to first find the complement of $81^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $81^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 81 \\y = 9$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for .

$\\180 = y + 9 \\y = 171$

So the answer is $171^{\circ}$ .

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Example Question #3 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $40^{\circ}$ ?

Possible Answers:

$50^{\circ}$

$80^{\circ}$

$130^{\circ}$

$140^{\circ}$

$40^{\circ}$

Correct answer:

$130^{\circ}$

Explanation:

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

We need to first find the complement of $40^{\circ}$ .

The complement is

90 = x + y

Since we are given an angle of $40^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 40 \\y = 50$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for .

$\\180 = y + 50 \\y = 130$

So the answer is $130^{\circ}$

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

What is the supplement of the complement of $66^{\circ}$ ?

Possible Answers:

$66^{\circ}$

$24^{\circ}$

$132^{\circ}$

$114^{\circ}$

$156^{\circ}$

Correct answer:

$156^{\circ}$

Explanation:

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

We need to first find the complement of $66^{\circ}$ .

The complement is

90 = x + y

Since we are given an angle of $66^{\circ}$ we can substitute it for $\uptext{x}$ , and solve for $\uptext{y}$ .

$\\90 = y + 66 \\y = 24$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for .

$\\180 = y + 24 \\y = 156$

So the answer is $156^{\circ}$

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Example Question #5 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $71^{\circ}$ ?

Possible Answers:

$19^{\circ}$

$109^{\circ}$

$161^{\circ}$

$142^{\circ}$

$71^{\circ}$

Correct answer:

$161^{\circ}$

Explanation:

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

We need to first find the complement of $71^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $71^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 71 \\y = 19$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for .

$\\180 = y + 19 \\y = 161$

So the answer is $161^{\circ}$

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Example Question #74 : Congruence

What is the supplement of the complement of $65^{\circ}$ ?

Possible Answers:

$65^{\circ}$

$130^{\circ}$

$115^{\circ}$

$25^{\circ}$

$155^{\circ}$

Correct answer:

$155^{\circ}$

Explanation:

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

We need to first find the complement of $65^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $65^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 65 \\y = 25$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for

$\\180 = y + 25 \\y = 155$

So the answer is $155^{\circ}$

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Example Question #75 : Congruence

What is the supplement of the complement of $45^{\circ}$ ?

Possible Answers:

$135^{\circ}$

$45^{\circ}$

$90^{\circ}$

$45^{\circ}$

Correct answer:

$135^{\circ}$

Explanation:

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

We need to first find the complement of $45^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $45^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 45 \\y = 45$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for

$\\180 = y + 45 \\y = 135$

So the answer is $135^{\circ}$ .

Report an Error

Example Question #8 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $76^{\circ}$ ?

Possible Answers:

$104^{\circ}$

$76^{\circ}$

$152^{\circ}$

$14^{\circ}$

$166^{\circ}$

Correct answer:

$166^{\circ}$

Explanation:

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

We need to first find the complement of $76^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $76^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 76 \\y = 14$

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

The supplement is

180 = x + y

Now we simply substitute the answer we just got for .

$\\180 = y + 14 \\y = 166$

So the answer is $166^{\circ}$ .

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Congruence

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #71 : Congruence

Example Question #72 : Congruence

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

Example Question #73 : Congruence

Example Question #3 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

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

Example Question #5 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #74 : Congruence

Example Question #75 : Congruence

Example Question #8 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

All Common Core: High School - Geometry Resources

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