Geometry: Triangles 161
What is true about the interior angles of triangles?
They add up to a sum of 180 degrees.
Which qualities are found in a triangle?
Three interior angles.
Which qualities are found in a triangle?
Three vertices.
What is the point at which two sides meet?
the vertex
Categorize this triangle:
1. Acute triangle 2. Equilateral triangle
What type of triangle has three unequal sides?
Scalene
Categorize this triangle:
1. Obtuse triangle 2. Scalene triangle
Categorize this triangle:
1. Right triangle 2. Isosceles triangle
When solving for the area of a triangle, by what must the base and height be multiplied?
1/2
A drawing of a triangle shows a 23° angle and a 56° angle. What is the measurement of the missing angle?
101°
The top and bottom sides of the enclosed figure are parallel, with a 58° angle in the upper right corner. What is the measurement of angle X?
122°
Angle X and the 19° angle are adjacent angles inside the right triangle. What is the measurement of angle X?
13 degrees
The 13° and 19° angles are adjacent angles inside the right triangle. What is the measurement of angle X?
58 degrees
A right triangle has an indicated 32° angle. What is the measurement of the missing angle?
58°
Assuming X is a right angle, what is the measurement of angle Y?
58°
A drawing of a triangle shows a 95° and a 17° angle. What is the measurement of the missing angle?
68°
A triangle has a 10 cm base and 15 cm height. What is the area of this triangle?
75 cm²
A right triangle has an indicated 14° angle. What is the measurement of the missing angle?
76°
The irregular pocket has edges indicated with 32° and 57° angles. What is the measurement of angle X?
91 degrees
Triangle
A closed figure with exactly three sides. The three sides meet to form three interior angles.
Perpendicular
A line that forms an angle of 90° with another line. The altitude of a triangle is perpendicular to the base.
Area
A measurement of the amount of space contained within a flat, enclosed shape. The area of a triangle is calculated as one half the base times the altitude (1/2 × b × a).
Vertex
A point where two lines or line segments meet or intersect. A triangle has three vertices.
Line
A series of points that extends endlessly in two directions. A line measures 180 degrees.
Right Triangle
A triangle containing exactly one 90 degree angle. The other two angles must total exactly 90 degrees.
Obtuse Triangle
A triangle containing one angle that is greater than 90 degrees. The other two angles must total less than 90 degrees.
Acute Triangle
A triangle containing three angles that each measure less than 90 degrees. All three angles must add up to 180 degrees.
Isosceles Triangle
A triangle that has two equal sides. An isosceles triangle also contains two equal angles.
Equilateral Triangle
A triangle with three equal sides that are the same length. Since all three sides of an equilateral triangle are the same length, all three angles must be equal.
Scalene Triangle
A triangle with three unequal sides. The angle opposite the longest side is the largest angle.
Which type of triangle contains three angles that measure less than 90°?
Acute
Altitude
Altitude is the line drawn perpendicular to the base that represents the height of a form. In a triangle, this line is drawn from the base to the opposite vertex.
Interior Angles
An angle located within a closed figure. A triangle has three interior angles.
An interior recess that is cut into the surface of a workpiece. Pockets may be round or rectangular.
Which statement is true about an equilateral triangle?
Each of the three interior angles equals 60 degrees.
Congruent
Equal or similar to each other. In an equilateral triangle, all sides are congruent to each other.
What type of triangle has sides with three equal lengths?
Equilateral
Based on the information in the sample shop drawing, what is true about angle X?
It is a right angle measuring 90 degrees.
Intersecting Lines
Lines that meet, cut across, or overlap. Two intersecting lines form the shape of an 'X' and create vertical angles.
What is the first step in solving for the area of a triangle that has a known base and height?
Multiply the values of the base and height together.
Which type of triangle contains an angle that measures larger than 90°?
Obtuse
Which statement is true about a right triangle?
One angle must measure exactly 90 degrees.
Which statement about adjacent angles is true? Adjacent angles:
Share a vertex on the same line.
Vertex Angle
The angle formed by the two legs of equal length in an isosceles triangle. The vertex angle is always opposite the base.
Base Angles
The angle that is formed by the base and one leg in an isosceles triangle. The base angles are always equal.
Which of the following statements about triangles is true? In any triangle, if two sides are equal:
The angles opposite those sides must be equal as well.
Which of the following statements is true about triangles? In every triangle, the largest side is opposite:
The largest angle in the triangle.
Sum
The resulting amount from combining or adding numbers together. The sum of interior angles of triangles is always 180 degrees.
Base
The side of a triangle from which the height is constructed. In an isosceles triangle, the base is the side that is not equal to the other sides.
Which statement is true about the angles in a triangle?
The sum of the interior angles always equals 180 degrees.
Legs
The two sides that are equal in length in an isosceles triangle. Since the legs of an isosceles triangle are equal in length, the angles opposite them must also be equal.
Which statement is true about a right triangle?
Two angles other than the right angle must total 90 degrees.
Vertical Angles
Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles have the same values and are formed whenever two lines intersect.
Adjacent Angles
Two angles that share the same vertex and one side. Adjacent angles do not overlap.
What symbol indicates a right angle in a triangle?
a small square
What is used to solve for unknown angles?
known angles
The top and bottom sides of the enclosed figure are parallel, with a 42° angle in the upper right corner. What is the measurement of angle X?
138 degrees
Consider the measurements of the triangle in the image. What is the area of the triangle?
140 square inches
A triangle has a base of 5.8 in. and a height of 9.75 in. What is the area of this triangle?
28.275 in.²
The irregular pocket has edges indicated with 91° and 57° angles. What is the measurement of angle X?
32 degrees
A triangle has two angles shown, measuring 110 and 37 degrees. What is the measurement of the third angle?
33
Consider the measurements of the triangle in the image. What is the area of the triangle?
35 square inches
Which of the following statements is true about adjacent angles? Adjacent angles:
share the same vertex on the same line.
