GEOMETRY QUESTIONS FOR SAT

Problem 1 :

In the figure below, x =

Solution

Problem 2 :

In the figure above, x = 2z and y = 3z . What is the value of z ?

(A) 24        (B) 30        (C) 36         (D) 54           (E) 60

Solution

Problem 3 :

In the figure above, what is in terms of y?

(A) 150 - y  (B) 150 + y   (C) 80 + y   (D) 30 + y   (E) 30 - x

Solution

Problem 4 :

The angles of a triangle are in the ratio of 2:3:4. What is the degree measure of the largest angle?

Solution

Problem 5 :

In the figure above, what is the value of a + b?

(A) 45     (B) 70       (C) 90       (D) 145   (E) 170

Solution

Problem 6 :

If two sides of a triangle are 8 and 5, each of the following could be the measure of the third side EXCEPT

(A) 4    (B) 5     (C) 8      (D) 12    (E) 13

Solution

Problem 7 :

 If the area of a right triangle is 15, what is its perimeter?

(A) 11      (B) 15      (C) 16      (D) 17

(E) The answer cannot be determined from the information provided.

Solution

Problem 9 : 

In the figure above, what is the area of right ?

(A) 4 √5     (B) 10     (C) 8 √5     (D) 20    (E) 40

Solution

Problem 9 :

In the figure above, if AD || BC, then x = 

(A) 20      (B) 30      (C) 50     (D) 60    (E) 70

Solution

Problem 10 :

What is the length of the hypotenuse of an isosceles right triangle with an area of 32?

(A) 4    (B) 4√2      (C) 8     (D) 8√2        (E) 3

Solution

Problem 11 :

What is the value of a above?

Solution

Problem 12 :

In shown above, if QS = 6, RS = 

(A) 12     (B) 6√3      (C) 6     (D) 3√3      (E) 3

Solution

Problem 13 :

The length of each side of a certain triangle is an even number. If no two of the sides have the same length, what is the smallest perimeter the triangle could have?

(A) 6     (B) 10      (C) 12      (D) 18     (E) 24

Solution