SAT Math : Acute / Obtuse Isosceles Triangles
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例子Questions
例子Question #1 :Isosceles Triangles
Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?
10
15
30
The answer cannot be determined
0
10
The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.
例子Question #3 :Isosceles Triangles
A triangle with two equal angles is called a(n)__________.
equilateral triangle
isosceles triangle
disjoint triangle
Pythagoras triangle
right triangle
isosceles triangle
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
例子Question #1 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
Triangle ABC has angle measures as follows:
What is
57
44
90
19
79
57
The sum of the measures of the angles of a triangle is 180.
Thus we set up the equation
After combining like terms and cancelling, we have
Thus
例子Question #2 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
Thus the vertex angle is 34 and the base angles are 73.
例子Question #3 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
The base angle of an isosceles triangle is 15 less than three times the vertex angle. What is the vertex angle?
Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
例子Question #4 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
The base angle of an isosceles triangle is ten less than twice the vertex angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
So the vertex angle is 40 and the base angles is 70
例子Question #1 :Isosceles Triangles
The base angle of an isosceles triangle is 10 more than twice the vertex angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
The vertex angle is 32 degrees and the base angle is 74 degrees
例子Question #6 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
In an isosceles triangle, the vertex angle is 15 less than the base angle. What is the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
Thus, 65 is the base angle and 50 is the vertex angle.
例子Question #7 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
In an isosceles triangle the vertex angle is half the base angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
例子Question #8 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
If the average (arithmetic mean) of two noncongruent angles of an isosceles triangle is
Since the triangle is isosceles, we know that 2 of the angles (that sum up to 180) must be equal. The question states that the noncongruent angles average 55°, thus providing us with a system of two equations:
Solving for x and y by substitution, we get x = 70° and y = 40° (which average out to 55°).
70 + 70 + 40 equals 180 also checks out.
Since 70° is not an answer choice for us, we know that the40°must be one of the angles.
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