### All PSAT Math Resources

## Example Questions

### Example Question #1 : Lines

Refer to the above figure. You are given that and . Which of the following statements would be sufficient to prove that is a right angle, given what is already known?

I)

II) and are both acute

III) is a right angle

**Possible Answers:**

I and II only

None of these

II and III only

I and III only

I, II, and III

**Correct answer:**

I and III only

If , then has short sides and long side . Since

,

then, by the converse of the Pythagorean Theorem, is a right triangle with right angle . Statement I is sufficient.

If and are both acute,we know nothing about ; every triangle has at least two acute angles regardless of type. Statement II tells us nothing.

and form a linear pair and are therefore supplementary. If one is a right angle, so is the other. Therefore, if is a right angle, so is . Statement III is sufficient.

The correct response is Statement I and III only.

### Example Question #1 : How To Find The Angle Of Two Lines

Note:

Refer to the above diagram. and which other angle form a pair of corresponding angles?

**Possible Answers:**

**Correct answer:**

Two angles formed by a transversal line crossing two other lines are corresponding angles if, relative to the points of intersection, they are in the same position. is formed by the intersection of transversal and ; the angle in the same relative position where intersects is .

### Example Question #3 : Lines

Refer to the above diagram. and which other angle form a pair of alternate interior angles?

**Possible Answers:**

**Correct answer:**

Two angles formed by a transversal line crossing two other lines are alternate interior angles if:

I) Both angles have their interiors between the lines crossed

II) The angles have their interiors on the opposite sides of the transversal.

Of the given choices, only fits the description; the interior of each is between and , and the interiors are on the opposite sides of .

### Example Question #4 : Lines

Refer to the above diagram.

and which other angle form a pair of vertical angles?

**Possible Answers:**

**Correct answer:**

Two angles are vertical angles if they share a vertex, anf if their union is a pair of intersecting lines. Of the five choices, only fits both descriptions with .

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