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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #3 : Plane Geometry

A student creates a challenge for his friend. He first draws a square, the adds the line for each of the 2 diagonals. Finally, he asks his friend to draw the circle that has the most intersections possible.

How many intersections will this circle have?

Possible Answers:

Correct answer:

Explanation:

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Example Question #1 : Geometry

Two pairs of parallel lines intersect:

Screen_shot_2013-03-18_at_10.29.11_pm

If A = 135^o, what is 2*|B-C| = ?

Possible Answers:

170°

160°

150°

180°

140°

Correct answer:

180°

Explanation:

By properties of parallel lines A+B = 180^o, B = 45^o, C = A = 135^o, so 2*|B-C| = 2* |45-135| = 180^o

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Example Question #2 : Geometry

Lines and are parallel. $\angle HFC=10^{\circ}$ , $\angle DGI=50^{\circ}$ , $\triangle EFG$ is a right triangle, and $\overline{EG}$ has a length of 10. What is the length of $\overline{EF}$

Possible Answers:

Not enough information.

Correct answer:

Explanation:

Since we know opposite angles are equal, it follows that angle $\angle AFE=10^{\circ}$ and $\angle BGE=50^{\circ}$ .

Imagine a parallel line passing through point . The imaginary line would make opposite angles with $\angle AFE$ & $\angle BGE$ , the sum of which would equal $\angle FEG$ . Therefore, $\angle FEG=60^{\circ}$ .

$\cos (60)=.5=\frac{EG}{EF}\rightarrow EF=\frac{EG}{.5}=20$

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Example Question #3 : Geometry

If $\angle A$ measures $(40-10x)^{\circ}$ , which of the following is equivalent to the measure of the supplement of $\angle A$ ?

Possible Answers:

$(10x+140)^{\circ}$

$(140-10x)^{\circ}$

$(10x+50)^{\circ}$

$(50-10x)^{\circ}$

$(100x)^{\circ}$

Correct answer:

$(10x+140)^{\circ}$

Explanation:

When the measure of an angle is added to the measure of its supplement, the result is always 180 degrees. Put differently, two angles are said to be supplementary if the sum of their measures is 180 degrees. For example, two angles whose measures are 50 degrees and 130 degrees are supplementary, because the sum of 50 and 130 degrees is 180 degrees. We can thus write the following equation:

$\dpi{100} measure\ of\ \angle A+ measure\ of\ supplement\ of\ \angle A=180$

$\dpi{100} 40-10x+ measure\ of\ supplement\ of\ \angle A=180$

Subtract 40 from both sides.

$\dpi{100} -10x+ measure\ of\ supplement\ of\ \angle A=140$

Add $\dpi{100} 10x$ to both sides.

$\dpi{100} measure\ of\ supplement\ of\ \angle A=140+10x=10x+140$

The answer is $(10x+140)^{\circ}$ .

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Example Question #781 : New Sat

In the following diagram, lines and are parallel to each other. What is the value for ?

Sat_math_166_03

Possible Answers:

60^o

30^o

It cannot be determined

100^o

80^o

Correct answer:

80^o

Explanation:

When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.

Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.

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Example Question #183 : Coordinate Geometry

The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle A. What is the sum, in degrees, of the measures of the supplement and complement of angle A?

Possible Answers:

190

140

Correct answer:

190

Explanation:

Let A represent the measure, in degrees, of angle A. By definition, the sum of the measures of A and its complement is 90 degrees. We can write the following equation to determine an expression for the measure of the complement of angle A.

A + measure of complement of A = 90

Subtract A from both sides.

measure of complement of A = 90 – A

Similarly, because the sum of the measures of angle A and its supplement is 180 degrees, we can represent the measure of the supplement of A as 180 – A.

The problem states that the measure of the supplement of A is 40 degrees larger than twice the measure of the complement of A. We can write this as 2(90-A) + 40.

Next, we must set the two expressions 180 – A and 2(90 – A) + 40 equal to one another and solve for A:

180 – A = 2(90 – A) + 40

Distribute the 2:

180 - A = 180 – 2A + 40

Add 2A to both sides:

180 + A = 180 + 40

Subtract 180 from both sides:

A = 40

Therefore the measure of angle A is 40 degrees.

The question asks us to find the sum of the measures of the supplement and complement of A. The measure of the supplement of A is 180 – A = 180 – 40 = 140 degrees. Similarly, the measure of the complement of A is 90 – 40 = 50 degrees.

The sum of these two is 140 + 50 = 190 degrees.

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Example Question #242 : New Sat Math Calculator

$\dpi{100} \small \overline{AB}$ is a straight line. $\dpi{100} \small \overline{CD}$ intersects $\dpi{100} \small \overline{AB}$ at point $\dpi{100} \small E$ . If $\dpi{100} \small \angle AEC$ measures 120 degrees, what must be the measure of $\dpi{100} \small \angle BEC$ ?

Possible Answers:

$\dpi{100} \small 75$ degrees

None of the other answers

$\dpi{100} \small 70$ degrees

$\dpi{100} \small 60$ degrees

$\dpi{100} \small 65$ degrees

Correct answer:

$\dpi{100} \small 60$ degrees

Explanation:

$\dpi{100} \small \angle AEC$ & $\dpi{100} \small \angle BEC$ must add up to 180 degrees. So, if $\dpi{100} \small \angle AEC$ is 120, $\dpi{100} \small \angle BEC$ (the supplementary angle) must equal 60, for a total of 180.

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Example Question #31 : Lines

Lines A and B are parallel. Find the measurement of $\angle1$ .

Possible Answers:

The measurement of $\angle1$ cannot be determined.

$102^\circ$

$78^\circ$

$180^\circ$

Correct answer:

$78^\circ$

Explanation:

When parallel lines are cut by a transversal, corresponding angles are congruent. The given angle and $\angle1$ are corresponding angles.

$\angle1$ must also have the same mesaurement as the given angle.

$\angle1=78^\circ$

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Example Question #32 : Lines

If lines A and B are parallel, what is the measurement of $\angle2$ ?

Possible Answers:

$44^\circ$

$78^\circ$

$102^\circ$

$95^\circ$

Correct answer:

$102^\circ$

Explanation:

$\angle2$ and the given angle are supplementary, meaning that their angle measurements add up to 180 .

$\angle2+78^\circ=180^\circ$

Subtracting 78 from each side to find the measurement of angle two.

$\angle2=102^\circ$

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Example Question #33 : Lines

If lines A and B are parallel, find the measurement for $\angle3$ .

Possible Answers:

$112^\circ$

$97^\circ$

$102^\circ$

$78^\circ$

Correct answer:

$102^\circ$

Explanation:

$\angle3$ and the given angle are supplementary, meaning that their angle measurements add up to 180 .

$\angle3+78^\circ=180^\circ$

Subtract 78 from both sides to find the measurement of angle 3.

$\angle3=102^\circ$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #3 : Plane Geometry

Example Question #1 : Geometry

Example Question #2 : Geometry

Example Question #3 : Geometry

Example Question #781 : New Sat

Example Question #183 : Coordinate Geometry

Example Question #242 : New Sat Math Calculator

Example Question #31 : Lines

Example Question #32 : Lines

Example Question #33 : Lines

All Basic Geometry Resources

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