### All Common Core: High School - Geometry Resources

## Example Questions

### Example Question #1 : Construct Basic Geometric Figures

What must occur to construct two angles from a angle?

**Possible Answers:**

Move the terminal ray of the angle up .

Move the nonterminal ray of the angle down .

Bisect the in half.

Move the terminal ray of the angle down .

Move the nonterminal ray of the angle up .

**Correct answer:**

Bisect the in half.

To construct two angles from a angle a bisection must occur. Recall that bisection means to cut an angle into two equal parts.

Since

that makes a bisection of the angle equal two angles and thus is the solution.

Moving the terminal ray will not create two angles and thus it cannot be the solution.

Nonterminal is not the correct terminology and therefore, it cannot be the correct solution.

### Example Question #211 : Congruence

How are congruent lines identified in a parallelogram?

**Possible Answers:**

One single hash mark on one line and a double hash mark on the parallel line

Double hash marks

Either single or double hash marks

Single hash marks

None of the other answers

**Correct answer:**

Either single or double hash marks

Parallel lines by definition are lines that will never intersect one another. This means the slope of the lines are the same. When these lines make up a parallelogram figures that are created include squares, rectangles, diamonds, and rhombi.

Some images that depict parallelograms are as follows. Notice that either single or double hash marks can be used to identify that opposite lines are congruent.

### Example Question #211 : Congruence

Given the point , how would perpendicular lines be constructed?

**Possible Answers:**

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

**Correct answer:**

Perpendicular lines are done by drawing a vertical line at and a horizontal line at .

To construct perpendicular lines first recall what it means to be perpendicular.

Recall that perpendicular lines intersect at one point and have opposite, reciprocal slopes.

Plotting the given point is as follows:

Given this point, there are numerous combinations of perpendicular lines that can be made. Looking at the possible options the only pair that intersect at the point is when a vertical line is drawn at and a horizontal line at .

### Example Question #581 : High School: Geometry

Determine whether the statement is true or false:

Lines that have fractional slopes cannot be perpendicular to other lines.

**Possible Answers:**

True

False

**Correct answer:**

False

For two lines to be perpendicular they must intersect at one point and have the opposite reciprocals on each other. Having slopes that are opposite reciprocals creates a angle between the two lines which is also by definition makes the two lines perpendicular.

Therefore, a line that has a fractional slope can also have a perpendicular line. If the line in question has a slope of then the perpendicular line would have a slope of .

Thus, the statement, "Lines that have fractional slopes cannot be perpendicular to other lines." is false.

### Example Question #212 : Congruence

Determine whether the statement is true or false:

An equilateral triangle must have sides of equal length but the interior angles may differ.

**Possible Answers:**

False

True

**Correct answer:**

False

By definition an equilateral triangle has all sides that are of equal length and angles are also equal. All interior angles on an equilateral triangle equal regardless of the side lengths.

Therefore, the statement "An equilateral triangle must have sides of equal length but the interior angles may differ." is false.

### Example Question #1 : Construct Basic Geometric Figures

Determine whether the statement is true or false:

In a parallelogram, opposite sides are always congruent.

**Possible Answers:**

False

True

**Correct answer:**

True

Using corresponding parts of congruent triangles proves this statement true.

A parallelogram is a four sided figure that has opposite parallel sides. Further more, when a parallelogram is divided into two triangles by drawing a line diagonally, they are equal triangles and thus the corresponding sides of each triangle are equal which in turn, makes the sides of the parallelogram congruent.