GEOMETRY PRACTICE PROBKEMS FOR SAT WORKSHEET

Problem 1 :

In the figure above, the perimeter of the triangle is 4 + 2√2. What is the value of x?

A) 2      B) 4    C) √2       D) 2√2     E) 2 + √2

Solution

Problem 2 :

If the five line segments in the figure above are all congruent, what is the ratio of the length of AC (not shown) to the length of BD?

A) √2 to 1     B) √3 to 1     C) √2 to 2

D) √3 to 2        E) √3 to √2

Solution

Problem 3 :

In the triangles above, what is the average (arithmetic mean) of u, v, w, x and y ?

A) 21    B) 45     C) 50      D) 52     E) 54

Solution

Problem 4 :

The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of △DEF is 10, what is the length of one side of △ABC?

A) 3 1/3         B) 10        C) 15     D) 30      E) 40

Solution

Problem 5 :

In the figure above, points P, A and B are equally spaced on line l and points P, Q and R are equally spaced on line m. If PB = 4, PR = 6, and AQ = 4, what is the perimeter of quadrilateral QABR?

A) 13        B) 14        C) 15        D) 16      E) 17

Solution

Problem 6 :

Solution

Problem 7 :

In the figure above, AE and CD are each perpendicular to CE. If x = y, the length of AB is 4, and the length of BD is 8, what is the length of CE?

A) 3√2      B) 6√2      C) 8√2     D) 10√2      E) 12√2

Solution

Problem 8 :

QR || PS in the figure above, what is the value (x + y) ?

A) 90        B) 120    C) 180      D) 270         E) 360

Solution

Problem 9 :

In the figure above, if the legs of triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC?

A) 2, 5, and √29       B) 2, 5, and 7      C) 3, 3 and 3√2

D) 3, 4 and 5       E) 4, 5 and √41

Solution

Problem 10 :

The figure above is a right triangle. What is the value of 49 + x² ?

A) 50         B) 51         C) 72         D) 98       E) 100

Solution