SAT Math : Triangles

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #135 : Sat Mathematics

Solve each problem and decide which is the best of the choices given.

 

Solve for .

 

 

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Possible Answers:

Correct answer:

Explanation:

To solve for , you must first solve for .

All triangles' angles add up to .

So subtract  from  to get , the value of .

Angles  and  are supplementary, meaning they add up to .

Subtract  from  to get .

, so .

Example Question #136 : Sat Mathematics

Triangle 2

Refer to the above figure. Evaluate .

Possible Answers:

Correct answer:

Explanation:

 is marked with three congruent sides, making it an equilateral triangle, so . This is an exterior angle of , making its measure the sum of those of its remote interior angles; that is, 

 has congruent sides  and , so, by the Isosceles Triangle Theorem, . Substituting   for  and  for :

 and  form a linear pair and are therefore supplementary - that is, their degree measures total . Setting up the equation 

and substituting:

 

Example Question #132 : Plane Geometry

Equilateral

Figure is not drawn to scale.

Refer to the provided figure. Evaluate .

Possible Answers:

Correct answer:

Explanation:

 is an equilateral, so all of its angles - in particular,   - measure . This angle is an exterior angle to ,  and its measure is equal to the sum of those of its two remote interior angles,  and , so 

Setting  and , solve for :

Example Question #1 : Acute / Obtuse Triangles

If a = 7 and b = 4, which of the following could be the perimeter of the triangle?

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I. 11

II. 15

III. 25

Possible Answers:

I Only

I and II Only

II Only

II and III Only

I, II and III

Correct answer:

II Only

Explanation:

Consider the perimeter of a triangle:

  P = a + b + c

Since we know a and b, we can find c. 

In I:

  11 = 7 + 4 + c

  11 = 11 + c 

  c = 0

Note that if c = 0, the shape is no longer a trial. Thus, we can eliminate I.

In II:

  15 = 7 + 4 + c

  15 = 11 + c

   c = 4.

This is plausible given that the other sides are 7 and 4. 

In III:

  25 = 7 + 4 + c

  25 = 11 + c

  c = 14.

It is not possible for one side of a triangle to be greater than the sum of both of the other sides, so eliminate III. 

Thus we are left with only II.

Example Question #141 : Sat Mathematics

Which of the following measurements can NOT represent the sides of a triangle. 

Possible Answers:

Correct answer:

Explanation:

Given the Triangle Inequality, the sum of any two sides of a triangle must be greater than the third side. 

Given the measurements :

Therefore, these lengths cannot represent a triangle. 

Example Question #142 : Sat Mathematics

If triangle ABC has vertices (0, 0), (6, 0), and (2, 3) in the xy-plane, what is the area of ABC?

Possible Answers:

10

20

12

9

18

Correct answer:

9

Explanation:

Sat-triangle

Sketching ABC in the xy-plane, as pictured here, we see that it has base 6 and height 3. Since the formula for the area of a triangle is 1/2 * base * height, the area of ABC is 1/2 * 6 * 3 = 9.

Example Question #141 : Geometry

The height, , of triangle  in the figure is one-fourth the length of . In terms of h, what is the area of triangle ?

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Possible Answers:

h^{2}

2h^{2}

\frac{1}{2}h^{2}

3h^{2}

Correct answer:

2h^{2}

Explanation:

If \dpi{100} \small h=\frac{1}{4} *\dpi{100} \small \overline{PQ}, then the length of \dpi{100} \small \overline{PQ} must be \dpi{100} \small 4h.

Using the formula for the area of a triangle (\frac{1}{2}bh), with \dpi{100} \small b=4h, the area of the triangle must be 2h^{2}.

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Find the height of a triangle if the area of the triangle = 18 and the base = 4.

Possible Answers:

1

6

9

4

Correct answer:

9

Explanation:

The area of a triangle = (1/2)bh where b is base and h is height. 18 = (1/2)4h which gives us 36 = 4h so h =9.

Example Question #141 : Sat Mathematics

 and  are similar triangles.  The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”.  If the perimeter of Triangle B is 135” and what are lengths of two of its sides?

Possible Answers:

Correct answer:

Explanation:

The perimeter is equal to the sum of the three sides.  In similar triangles, each side is in proportion to its correlating side.  The perimeters are also in equal proportion.

Perimeter A = 45” and perimeter B = 135”

The proportion of Perimeter A to Perimeter B is

This applies to the sides of the triangle.  Therefore to get the any side of Triangle B, just multiply the correlating side by 3.

15” x 3 = 45”

10” x 3 = 30“

 

 

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Example Question #1 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

A triangle has sides of length 8, 13, and L. Which of the following cannot equal L?

Possible Answers:

4

15

6

7

9

Correct answer:

4

Explanation:

The sum of the lengths of two sides of a triangle cannot be less than the length of the third side. 8 + 4 = 12, which is less than 13.

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