Triangles - Geometry
Card 0 of 1188
An obtuse triangle has a base of 
and an area of 
square units. Find the height of the triangle.
An obtuse triangle has a base of
To solve this solution, first work backwards using the formula:
Plugging in the given values we are able to solve for the height.
To solve this solution, first work backwards using the formula:
Plugging in the given values we are able to solve for the height.
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Refer to the above diagram. 
.
True or false: From the information given, it follows that 
.
Refer to the above diagram.
True or false: From the information given, it follows that
By the Angle-Angle Similarity Postulate, if two pairs of corresponding angles of a triangle are congruent, the triangles themselves are similar.
and 
are a pair of vertical angles, having the same vertex and having sides opposite each other. As such, 
.
and 
are alternating interior angles formed by two parallel lines 
and 
cut by a transversal 
. As a consequence, 
.
The conditions of the Angle-Angle Similarity Postulate are satisfied, and it holds that 
.
By the Angle-Angle Similarity Postulate, if two pairs of corresponding angles of a triangle are congruent, the triangles themselves are similar.
The conditions of the Angle-Angle Similarity Postulate are satisfied, and it holds that
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Two of the exterior angles of a triangle, taken at different vertices, measure 
. Is the triangle acute, right, or obtuse?
Two of the exterior angles of a triangle, taken at different vertices, measure
At a given vertex, an exterior angle and an interior angle of a triangle form a linear pair, making them supplementary - that is, their measures total 
. The measures of two interior angles can be calculated by subtracting the exterior angle measures from :
The triangle has two interior angles of measure 
.
The measures of the interior angles of a triangle add up to . If 
is the measure of the third angle, then
All three interior angles measure less than 
, making them acute. The triangle is, by definition, acute.
At a given vertex, an exterior angle and an interior angle of a triangle form a linear pair, making them supplementary - that is, their measures total
The triangle has two interior angles of measure
The measures of the interior angles of a triangle add up to
All three interior angles measure less than
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Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths 
mm and 
mm. What are possible measurements for the corresponding sides in triangle two?
Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths
Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.
The ratio of triangle one is:
If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:
Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.
The ratio of triangle one is:
If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:
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Find the height of the triangle shown above.
Find the height of the triangle shown above.
Use the Pythagorean Theorem to find the height of this triangle: 
, where 
the height of the triangle.
Use the Pythagorean Theorem to find the height of this triangle:
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Find the height of the obtuse triangle shown above.
Find the height of the obtuse triangle shown above.
To solve this solution, first work backwards using the formula:
Plugging in the given values we are able to solve for the height.
To solve this solution, first work backwards using the formula:
Plugging in the given values we are able to solve for the height.
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Find the height of the acute triangle shown above.
Find the height of the acute triangle shown above.
To solve this solution, work backwards using the formula:
Plugging in the given values we are able to solve for the height.
To solve this solution, work backwards using the formula:
Plugging in the given values we are able to solve for the height.
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Find the value of 
if the perimeter is 
.
Find the value of
The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is 
also.
Now, use the information given about the perimeter to set up an equation to solve for 
. The sum of all the sides will give the perimeter.
The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is
Now, use the information given about the perimeter to set up an equation to solve for
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and 
are both isosceles triangles;
True or false: from the given information, it follows that 
.
True or false: from the given information, it follows that
As we are establishing whether or not 
, then 
, 
, and 
correspond respectively to 
, 
, and 
.
is an isosceles triangle, so it must have two congruent angles. 
has measure 
, so either 
has this measure, 
has this measure, or 
. If we examine the second case, it immediately follows that 
. One condition of the similarity of triangles is that all pairs of corresponding angles be congruent; since there is at least one case that violates this condition, it does not necessarily follow that 
. This makes the correct response "false".
As we are establishing whether or not
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An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
A triangle has 
degrees. An isoceles triangle has one vertex angle and two congruent base angles.
Let 
= the base angle and 
= vertex angle
So the equation to solve becomes 
or
so the base angle is 
and the vertex angle is 
and the difference is 
.
A triangle has
Let
So the equation to solve becomes
or
so the base angle is
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An ssosceles triangle has interior angles of 
degrees and 
degrees. Find the missing angle.
An ssosceles triangle has interior angles of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
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The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the two equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
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The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of 
degrees. Find the measurement of the obtuse angle.
The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
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In an obtuse isosceles triangle the angle measurements are, 
, 
, and 
. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the angle measurements are,
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
However, 
degrees is the measurement of both of the acute angles combined.
Each individual angle is 
.
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
However,
Each individual angle is
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In an acute isosceles triangle the two equivalent interior angles each have a measurement of 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles each have a measurement of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
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In an acute isosceles triangle the two equivalent interior angles are each 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles are each
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
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The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse Isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
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In an obtuse isosceles triangle the largest angle is 
degrees. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the largest angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
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In an acute isosceles triangle the measurement of the non-equivalent interior angle is 
degrees. Find the measurement of one of the equivalent interior angles.
In an acute isosceles triangle the measurement of the non-equivalent interior angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
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In an obtuse isosceles triangle, the largest interior angle is 
degrees. What is the measurement of one of the equivalent interior angles?
In an obtuse isosceles triangle, the largest interior angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
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