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SAT Math : Triangles

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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 .

Untitled

Possible Answers:

x=20

x=180

x=60

x=120

x=40

Correct answer:

x=20

Explanation:

To solve for , you must first solve for .

All triangles' angles add up to $180$^{\circ}$$ .

So subtract (40+20) from 180 to get 120 , the value of .

Angles and are supplementary, meaning they add up to 180 .

Subtract 180 from 120 to get $60$^{\circ}$$ .

$3x=60$^{\circ}$$ , so $x=20$^{\circ}$$ .

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Example Question #132 : Sat Mathematics

Triangle 2

Refer to the above figure. Evaluate $m \angle CDE$ .

Possible Answers:

$120^{\circ}$

$150 ^{\circ }$

$144^{\circ }$

$135^{\circ }$

$162 ^{\circ }$

Correct answer:

$150 ^{\circ }$

Explanation:

$\bigtriangleup ABC$ is marked with three congruent sides, making it an equilateral triangle, so $m \angle ABC = 60 ^{\circ }$ . This is an exterior angle of $\bigtriangleup BCD$ , making its measure the sum of those of its remote interior angles; that is,

$m \angle BCD + m \angle BDC = m \angle ABC$

$\bigtriangleup BCD$ has congruent sides $\overline{BC}$ and $\overline{CD}$ , so, by the Isosceles Triangle Theorem, $m \angle BCD = m \angle BDC$ . Substituting $m \angle BDC$ for $m \angle BCD$ and $60 ^{\circ }$ for $m \angle ABC$ :

$m \angle BDC + m \angle BDC = 60 ^{\circ }$

$2 \cdot m \angle BDC = 60 ^{\circ }$

$m \angle BDC = 30 ^{\circ }$

$\angle BDC$ and $\angle CDE$ form a linear pair and are therefore supplementary - that is, their degree measures total $180 ^{\circ }$ . Setting up the equation

$m \angle BDC + m\angle CDE= 180 ^{\circ }$

and substituting:

$30 ^{\circ } + m\angle CDE= 180 ^{\circ }$

$m\angle CDE= 150 ^{\circ }$

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Example Question #132 : Plane Geometry

Equilateral

Figure is not drawn to scale.

Refer to the provided figure. Evaluate $m \angle CAD$ .

Possible Answers:

$13^{\circ}$

$18^{\circ }$

$8^{\circ }$

$28^{\circ }$

$23^{\circ }$

Correct answer:

$18^{\circ }$

Explanation:

$\bigtriangleup ABC$ is an equilateral, so all of its angles - in particular, $\angle ACB$ - measure $60^{\circ }$ . This angle is an exterior angle to $\bigtriangleup DAC$ , and its measure is equal to the sum of those of its two remote interior angles, $\angle DAC$ and $\angle D$ , so

$m\angle DAC + m\angle D = m \angle ACB$

Setting $m \angle ACB =60^{ \circ}$ and $m \angle D = 42^{\circ }$ , solve for $m\angle DAC$ :

$m\angle DAC + 42^{\circ }= 60^{\circ }$

$m\angle DAC = 60^{\circ } - 42^{\circ }= 18^{\circ }$

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Example Question #111 : Triangles

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

Msp30320bea9chb26d18hh0000627i1e4ibba8c4f5

I. 11

II. 15

III. 25

Possible Answers:

I Only

I and II Only

II and III Only

I, II and III

II Only

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.

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Example Question #112 : Triangles

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

Possible Answers:

12, 13, 26

2, 3, 4

10, 14, 25

3, 5, 6

7, 8, 17

Correct answer:

12, 13, 26

Explanation:

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

Given the measurements 12, 13, 26 :

$12 + 13 \ngtr 26$

Therefore, these lengths cannot represent a triangle.

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Example Question #335 : Plane Geometry

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

Possible Answers:

Correct answer:

Explanation:

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.

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

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

Possible Answers:

$h^{2}$

$3h^{2}$

$2h^{2}$

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

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 $2h^{2}$ .

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Example Question #143 : Sat Mathematics

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

Possible Answers:

Correct answer:

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.

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Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\text{Triangle A}$ and $\text{Triangle B}$ 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:

${4}''\textup{ and }{6}''$

${20}''\textup{ and }{30}''$

${13}''\textup{ and }{19}''$

${30}''\textup{ and }{45}''$

Correct answer:

${30}''\textup{ and }{45}''$

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 $\frac{45}{135}=\frac{1}{3}$ .

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“

Screen shot 2016 02 16 at 10.45.30 am

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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:

Correct answer:

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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SAT Math : Triangles

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #135 : Sat Mathematics

Example Question #132 : Sat Mathematics

Example Question #132 : Plane Geometry

Example Question #111 : Triangles

Example Question #112 : Triangles

Example Question #335 : Plane Geometry

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

Example Question #143 : Sat Mathematics

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

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

All SAT Math Resources

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