How to find the length of the side of of an acute / obtuse isosceles triangle - Math
Card 0 of 40
Given 
such that 
, 
, 
, which of the following statements is true?
Given
Having three sides of different lengths, this triangle is scalene. In any scalene triangle, the angle with greatest measure is opposite the longest side, and the angle with least measure is opposite the shortest side. Therefore, since 
, their opposite angles would be in order from greatest to least measure - that is, 
.
Having three sides of different lengths, this triangle is scalene. In any scalene triangle, the angle with greatest measure is opposite the longest side, and the angle with least measure is opposite the shortest side. Therefore, since
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Find the perimeter of the triangle below.
Find the perimeter of the triangle below.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
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Find the perimeter of the triangle below.
Find the perimeter of the triangle below.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
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If a triangle has side lengths of 
and 
, which of the following can be a length of the third side?
If a triangle has side lengths of
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of 
is the only choice that fits this criteria:
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of
Compare your answer with the correct one above
If a triangle has side lengths of 
and 
, which of the following could be the length of the third side?
If a triangle has side lengths of
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of 
is the only choice that fits this criteria:
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of
Compare your answer with the correct one above
A triangle has sides of lengths 14, 18, and 20. Is the triangle scalene or isosceles?
A triangle has sides of lengths 14, 18, and 20. Is the triangle scalene or isosceles?
A triangle with three sides of different length is, by definition, scalene.
A triangle with three sides of different length is, by definition, scalene.
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Given: Regular Pentagon 
with center 
. Construct segments 
and 
to form 
.
True or false: 
is an isosceles triangle.
Given: Regular Pentagon
True or false:
Below is regular Pentagon 
with center 
, a segment drawn from 
to each vertex - that is, each of its radii drawn.
By symmetry, all of the radii of a regular pentagon are congruent - specifically, 
. This triangle has at least two congruent sides, so it is isosceles.
Below is regular Pentagon
By symmetry, all of the radii of a regular pentagon are congruent - specifically,
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Refer to the above triangle. By what statement does it follow that 
?
Refer to the above triangle. By what statement does it follow that
We are given that, in 
, two angles are congruent; specifically, 
. It is a consequence of the Converse of the Isosceles Triangle Theorem that the sides opposite the angles are also congruent - that is, .
.
We are given that, in
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Figure NOT drawn to scale.
Refer to the above diagram.
True or false: 
.
Figure NOT drawn to scale.
Refer to the above diagram.
True or false:
The sum of the measures of the interior angles of a triangle is 
, so
Substitute the given two angle measures and solve for 
:
Subtract 
from both sides:
, so, by the Converse of the Isosceles Triangle Theorem, their opposite sides are also congruent - that is,
The sum of the measures of the interior angles of a triangle is
Substitute the given two angle measures and solve for
Subtract
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A triangle has a perimeter of 
inches with one side of length 
inches. If the remaining two sides have lengths in a ratio of 
, what is length of the shortest side of the triangle?
A triangle has a perimeter of
The answer is 
.
Since we know that the permieter is 
inches and one side is 
inches, it can be determined that the remaining two sides must combine to be 
inches. The ratio of the remaining two sides is 
which means 3 parts : 4 parts or 7 parts combined. We can then set up the equation 
, and divide both sides by 
which means 
. The ratio of the remaining side lengths then becomes 
or 
. We now know the 3 side lengths are 
.
is the shortest side and thus the answer.
The answer is
Since we know that the permieter is
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Given such that , , , which of the following statements is true?
Given
Having three sides of different lengths, this triangle is scalene. In any scalene triangle, the angle with greatest measure is opposite the longest side, and the angle with least measure is opposite the shortest side. Therefore, since , their opposite angles would be in order from greatest to least measure - that is, .
Having three sides of different lengths, this triangle is scalene. In any scalene triangle, the angle with greatest measure is opposite the longest side, and the angle with least measure is opposite the shortest side. Therefore, since
Compare your answer with the correct one above
Find the perimeter of the triangle below.
Find the perimeter of the triangle below.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Compare your answer with the correct one above
Find the perimeter of the triangle below.
Find the perimeter of the triangle below.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Use the Pythagorean Theorem to find the base of the right triangle.
Now, because two of the angles in this triangle are the same, this is an isosceles triangle. In an isosceles triangle, the sides that are directly across from the congruent angles are also congruent.
In addition, the height in an isosceles triangle will always cut the 3rd side in half. With this information, fill out the triangle as shown below:
To find the perimeter, add up all the sides.
Compare your answer with the correct one above
If a triangle has side lengths of and , which of the following can be a length of the third side?
If a triangle has side lengths of
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of is the only choice that fits this criteria:
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of
Compare your answer with the correct one above
If a triangle has side lengths of and , which of the following could be the length of the third side?
If a triangle has side lengths of
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of is the only choice that fits this criteria:
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. The relationship can be represented by the following inequalities:
The side length of
Compare your answer with the correct one above
A triangle has sides of lengths 14, 18, and 20. Is the triangle scalene or isosceles?
A triangle has sides of lengths 14, 18, and 20. Is the triangle scalene or isosceles?
A triangle with three sides of different length is, by definition, scalene.
A triangle with three sides of different length is, by definition, scalene.
Compare your answer with the correct one above
Given: Regular Pentagon with center . Construct segments and to form .
True or false: is an isosceles triangle.
Given: Regular Pentagon
True or false:
Below is regular Pentagon with center , a segment drawn from to each vertex - that is, each of its radii drawn.
By symmetry, all of the radii of a regular pentagon are congruent - specifically, . This triangle has at least two congruent sides, so it is isosceles.
Below is regular Pentagon
By symmetry, all of the radii of a regular pentagon are congruent - specifically,
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Refer to the above triangle. By what statement does it follow that ?
Refer to the above triangle. By what statement does it follow that
We are given that, in , two angles are congruent; specifically, . It is a consequence of the Converse of the Isosceles Triangle Theorem that the sides opposite the angles are also congruent - that is, ..
We are given that, in
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Figure NOT drawn to scale.
Refer to the above diagram.
True or false: .
Figure NOT drawn to scale.
Refer to the above diagram.
True or false:
The sum of the measures of the interior angles of a triangle is , so
Substitute the given two angle measures and solve for :
Subtract from both sides:
, so, by the Converse of the Isosceles Triangle Theorem, their opposite sides are also congruent - that is,
The sum of the measures of the interior angles of a triangle is
Substitute the given two angle measures and solve for
Subtract
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A triangle has a perimeter of inches with one side of length inches. If the remaining two sides have lengths in a ratio of , what is length of the shortest side of the triangle?
A triangle has a perimeter of
The answer is .
Since we know that the permieter is inches and one side is inches, it can be determined that the remaining two sides must combine to be inches. The ratio of the remaining two sides is which means 3 parts : 4 parts or 7 parts combined. We can then set up the equation , and divide both sides by which means . The ratio of the remaining side lengths then becomes or . We now know the 3 side lengths are .
is the shortest side and thus the answer.
The answer is
Since we know that the permieter is
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