高School Math : Triangles
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Example Questions
Example Question #1 :Isosceles Triangles
An isosceles triangle has a base of
Example Question #1 :How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle
One side of an acute isosceles triangle is 15 feet. Another side is 5 feet. What is the perimeter of the triangle in feet?
Because this is an acute isosceles triangle, the third side must be the same as the longer of the sides that you were given. To find the perimeter, multiply the longer side by 2 and add the shorter side.
Example Question #3 :Acute / Obtuse Isosceles Triangles
An isoceles triangle has a base angle five more than twice the vertex angle. What is the difference between the base angle and the vertex angle?
A triangle has 180 degrees. An isoceles triangle has one vertex angle and two congruent base angles.
Let
So the equation to solve becomes
So the vertex angle is
Example Question #1 :Isosceles Triangles
Points A and B lie on a circle centered at Z, where central angle
15°
30°
20°
Cannot be determined from the given information
25°
20°
Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with 140 + 2x = 180-->2x = 40-->x = 20
Example Question #2011 :Hspt Mathematics
Triangle FGH has equal lengths for FG and GH; what is the measure of∠F, if∠G measures 40 degrees?
None of the other answers
140 degrees
70 degrees
100 degrees
40 degrees
70 degrees
It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.
Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means∠F =∠H, and that∠F +∠H + 40 = 180,
By substitution we find that∠F * 2 = 140 and angle F = 70 degrees.
Example Question #1 :Isosceles Triangles
The vertex angle of an isosceles triangle is
An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains
Example Question #1421 :Concepts
In an isosceles triangle the base angle is five less than twice the vertex angle. What is the sum of the vertex angle and the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let
and
So the equation to solve becomes
or
Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.
Example Question #31 :Isosceles Triangles
Sides
This triangle has an angle of
Example Question #1 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
An isosceles triangle has a vertex angle that is twenty degrees more than twice the base angle. What is the sum of the vertex and base angles?
40
All triangles contain
Let
So the equation to solve becomes
We get
Example Question #10 :Acute / Obtuse Isosceles Triangles
If an isosceles triangle has an angle measuring greater than 100 degrees, and another angle with a measuring
In order for a triangle to be an isosceles triangle, it must contain two equivalent angles and one angle that is different. Given that one angle is greater than 100 degrees:
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