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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

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $48^{\circ}$ ?

Possible Answers:

$138^{\circ}$

$132^{\circ}$

$48^{\circ}$

$42^{\circ}$

$96^{\circ}$

Correct answer:

$138^{\circ}$

Explanation:

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

We need to first find the complement of $48^{\circ}$ .

The complement is

90 = x + y

Since we are given an angle of $48^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 48 \\y = 42$

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 .

$\\180 = y + 42 \\y = 138$

So the answer is $138^{\circ}$

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Example Question #7 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $4^{\circ}$ ?

Possible Answers:

$94^{\circ}$

$176^{\circ}$

$86^{\circ}$

$8^{\circ}$

$4^{\circ}$

Correct answer:

$94^{\circ}$

Explanation:

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

We need to first find the complement of $4^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $4^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 4 \\y = 86$

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 .

$\\180 = y + 86 \\y = 94$

So the answer is $94^{\circ}$

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Example Question #11 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $18^{\circ}$ ?

Possible Answers:

$72^{\circ}$

$18^{\circ}$

$162^{\circ}$

$108^{\circ}$

$36^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

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

We need to first find the complement of $18^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $18^{\circ}$ we can substitute it for $\uptext{x}$ , and solve for $\uptext{y}$ .

$\\90 = y + 18 \\y = 72$

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 .

$\\180 = y + 72 \\y = 108$

So the answer is $108^{\circ}$ .

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Example Question #12 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $62^{\circ}$ ?

Possible Answers:

$124^{\circ}$

$152^{\circ}$

$118^{\circ}$

$28^{\circ}$

$62^{\circ}$

Correct answer:

$152^{\circ}$

Explanation:

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

We need to first find the complement of $62^{\circ}$

The complement is

90 = x + y

Since we are given an angle of $62^{\circ}$ we can substitute it for , and solve for .

$\\90 = y + 62 \\y = 28$

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 .

$\\180 = y + 28 \\y = 152$

So the answer is $152^{\circ}$ .

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Example Question #1 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

Hsg.co.c.10 q1

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.

Hsg.co.c.10 q1

Looking at the triangles the corresponding angles are equal and the correspond side is also equal therefore, the triangles are congruent.

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Example Question #2 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

Hsg.co.c.10 q2

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Hsg.co.c.10 q2

Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.

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Example Question #81 : Congruence

Are the two triangles congruent?

Hsg.co.c.10 q3

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Hsg.co.c.10 q3

Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.

Report an Error

Example Question #4 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

Hsg.co.c.10 q4

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Hsg.co.c.10 q4

Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.

Report an Error

Example Question #5 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles shown congruent?

Hsg.co.c.10 q5

Possible Answers:

Yes

Correct answer:

Explanation:

Hsg.co.c.10 q5

Looking at the triangles the corresponding angles are not equal and the correspond side is also not equal therefore, the triangles are not congruent.

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Example Question #6 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Are the two triangles congruent?

Hsg.co.c.10 q7

Possible Answers:

Yes

Correct answer:

Explanation:

For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.

Hsg.co.c.10 q7

Looking at the triangles the corresponding sides are not equal therefore, the triangles are not congruent.

Report an Error

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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 #6 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #7 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #11 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #12 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #1 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Example Question #2 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Example Question #81 : Congruence

Example Question #4 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Example Question #5 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

Example Question #6 : Prove Triangle Theorems: Ccss.Math.Content.Hsg Co.C.10

All Common Core: High School - Geometry Resources

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