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Common Core: High School - Geometry : High School: Geometry

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 #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for c.

If both sides are equal, then the side lengths result in a right triangle.

$\\2 ^2+ 3 ^2= 6 ^2 \\4 + 9 = 36 \\13 = 36$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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Example Question #3 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\\3 ^2+ 4 ^2= 11 ^2 \\9 + 16 = 121 \\25 = 121$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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Example Question #4 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\\1 ^2+ 2 ^2= 4 ^2 \\1 + 4 = 16 \\5 = 16$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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Example Question #5 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\\7 ^2+ 8 ^2= 9 ^2 \\49 + 64 = 81 \\113 = 81$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\\1 ^2+ 2 ^2= 11 ^2 \\1 + 4 = 121 \\5 = 121$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

Report an Error

Example Question #11 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths , , and is a right triangle.

Possible Answers:

Yes

Correct answer:

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\\1 ^2+ 2 ^2= 14 ^2 \\1 + 4 = 196 \\5 = 196$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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Example Question #161 : High School: Geometry

Determine whether a triangle with side lengths 5, 12, and 13 is a right triangle.

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in 5 for , 12 for , and 13 for .

If both sides are equal, then the side lengths result in a right triangle.

5² + 12² = 13²

25 + 144 = 169

169 = 169

Since both sides are equal, we can conclude that this is a right triangle.

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Example Question #1 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

The Law of Cosines is a generalization of which common theorem?

Possible Answers:

Pythagorean Theorem

Triangle Sum Theorem

Side Angle Side Similarity Theorem

Triangle Proportionality Theorem

Fundamental Theorem of Algebra

Correct answer:

Pythagorean Theorem

Explanation:

The Law of Cosines is a generalization of the Pythagorean Theorem. To better understand this, start by drawing triangle ABC with sides a, b, and c. Then, construct the altitude from point A to get height h. Finally label the distance between point B and the point where h meets side a as distance r.

Screen shot 2020 07 01 at 7.58.05 pm

We will arbitrarily work to solve for side b, but we could do the same for a and c (after drawing the correct altitudes), which is why we can generalize that the other two formulas to find a and c follow.

By definition, we know that $\sin\angle B= \frac{h}{c}$ . If we multiply both sides by c, we get $c\sin\angle B= h$ .

Also, we know that $\cos\angle B= \frac{r}{c}$ . If we multiply both sides by c, we get $c\cos\angle B= r$ .

Using the Pythagorean Theorem, we get b^2=h^2+(a-r)^2 .

Substituting in h and r from above, we get:

$b^2=(c\sin \angle B)^2+ (a-c\cos\angle B)^2$

$= c^2\sin^2 \angle B + a^2-2ac\cos\angle B + c^2\cos^2\angle B$

$= c^2 (sin^2 \angle B+cos^2\angle B) + a^2-2ac\cos\angle B$ (because $sin^2 \angle B+cos^2\angle B=1$ )

$= c^2 + a^2-2ac\cos\angle B$

Therefore $b^2= c^2 + a^2-2ac\cos\angle B$ .

The other two versions of Law of Cosines are:

$a^2= b^2 + c^2-2bc\cos\angle A$

$c^2= a^2 + b^2-2ab\cos\angle C$

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Example Question #2 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

True or false: The Law of Sines applies to all types of triangles.

Possible Answers:

True

False

Correct answer:

True

Explanation:

This is true. While the Pythagorean Theorem only applies to right triangles, the Law of Sines applies to all triangles no matter if they are right, acute, or obtuse.

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Example Question #1 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

True or False: The Law of Cosines applies to all triangles.

Possible Answers:

True

False

Correct answer:

True

Explanation:

This is true. While the Pythagorean Theorem only applies to right triangles, the Law of Cosines applies to all triangles no matter if they are right, acute, or obtuse.

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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

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Common Core: High School - Geometry : High School: Geometry

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #3 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #4 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #5 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #11 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Example Question #161 : High School: Geometry

Example Question #1 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

Example Question #2 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

Example Question #1 : Prove Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.10

All Common Core: High School - Geometry Resources

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