### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #11 : Plane Geometry

Given and with

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is greater.

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

**Correct answer:**

It is impossible to tell from the information given.

Examine the diagram below, in which two triangles matching the given descriptions have been superimposed.

Note that and . The two question marks need to be replaced by and . No matter how you place these two points, . However, with one replacement, ; with the other replacement, . Therefore, the information given is insufficient to answer the question.

### Example Question #12 : Geometry

Consider and with .

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

**Correct answer:**

(a) and (b) are equal.

, so, by the Side-Side-Side Principle, since there are three pairs of congruent corresponding sides between the triangles, we can say they are congruent - that is,

.

Corresponding angles of congruent sides are congruent, so .