Geometric figures
Equiangular Triangle
A triangle with three congruent angles.
Equilateral Triangle
A triangle with three congruent sides.
Exterior Angle of Triangle
An angle that forms a linear pair with an interior angle of the triangle.
Right Angle
An angle with measure of 90 degrees.
SSS
Are the triangles congruent? If yes, why?
Isosceles
Classify the triangle by side lengths.
Triangle
Corner Cut- Cube
Rectangle
Corner Cut- Rectangular Prism
Trapezoid
Corner Cut- Square Pyramid
90
Definition of Perpendicular: Perpendicular lines form ___ degree angles.
Ellipse
Diagonal Cut- Cone
Rectangle
Diagonal Cut- Cube
Ellipse
Diagonal Cut- Cylinder
Rectangle
Diagonal Cut- Rectangular Prism
c + 34 + 120 = 180 c + 154 = 180 c = 26 26 degrees
Find the measure of angle C.
y + 42 + 42 = 180 y + 84 = 180 y = 96
Find the measure of angle Y.
x = 66 y = 180 - 66 - 66 y = 48
Find x and y.
3x = 60 x = 20 4y = 60 y = 15 5z = 60 z = 12
Find x, y and z.
(4x + 2) + (2x - 9) = 5x + 13 6x - 7 = 5x + 13 x - 7 = 13 x = 20
Find x.
25 + (x + 15) = 3x - 10 x + 40 = 3x - 10 40 = 2x - 10 50 = 2x 25 = x or x = 25
Find x.
2x + 3x = 100 5x = 100 x = 20
Find x.
4x = 60 x = 15
Find x.
5y - 6 = 4y + 12 y - 6 = 12 y = 18
Find y.
Hemisphere
Half of a sphere
3
How many interior angles does a triangle have?
Angle X
Name the angle included by segments XY and XZ.
Angle Z
Name the angle included by segments XZ and YZ.
Angle Y
Name the angle included by segments YZ and XY.
segment AB
Name the side included by angles A and B.
Segment AC
Name the side included by angles A and C.
Segment BC
Name the side included by angles B and C.
Circle
Parallel Cut
Hexagon
Parallel Cut
Pentagon
Parallel Cut
Circle
Parallel Cut To Base- Cone
Square
Parallel Cut To Base- Cube
Circle
Parallel Cut To Base- Cylinder
Rectangle
Parallel Cut To Base- Rectangular Prism
Square
Parallel Cut To Base- Square Pyramid
Triangle
Parallel Cut To Base- Triangular Prism
Triangle
Parallel Cut To Base- Triangular Pyramid
Square
Parallel Cut- Cube
Circle
Parallel Cut- Sphere
Square
Parallel Cut- Square pyramid
Triangle
Parallel Cut- Triangular Prism
Circle
Perpendicular Cut
Rectangle
Perpendicular Cut
Semicircle
Perpendicular Cut
Triangle
Perpendicular Cut
Triangle
Perpendicular Cut To Base- Cone
Square
Perpendicular Cut To Base- Cube
Rectangle
Perpendicular Cut To Base- Cylinder
Rectangle
Perpendicular Cut To Base- Rectangular Prism
Triangle
Perpendicular Cut To Base- Square Pyramid
Rectangle
Perpendicular Cut To Base- Triangular Prism
Triangle
Perpendicular Cut To Base- Triangular Pyramid
Square
Perpendicular Cut- Cube
Circle
Perpendicular Cut- Sphere
Triangle
Perpendicular Cut- Square pyramid
Rectangle
Perpendicular Cut- Triangular Prism
Reflexive Property
Reason an angle or segment is congruent to itself.
congruent
Right Angle Congruence Thm: Right angles are ____.
90
The acute angle measures of a right triangle have a sum of ___ degrees.
obtuse and scalene
The interior angle measures of a triangle are 16, 100, and 64 degrees. The triangle is ___ and ___.
180
The interior angle sum of a triangle is ___ degrees.
smaller angle: x larger angle: 4x x + 4x = 90 x = 18 18 degrees
The measure of one acute angle in a right triangle is 4 times the measure of the other acute angle. What is the measure of the smaller angle?
smaller angle: x larger angle: 5x x + 5x = 90 x = 15 15 degrees
The measure of one acute angle in a right triangle is 5 times the measure of the other acute angle. What is the measure of the smaller angle?
smaller angle: x larger angle: 8x x + 8x = 90 x = 10 10 degrees
The measure of one acute angle in a right triangle is 8 times the measure of the other acute angle. What is the measure of the smaller angle?
congruent
Vertical Angles Theorem: Vertical angles are ___.
Cylinder
a solid with congruent circular bases that lie in parallel planes
Square Prism
the bases of the prism are square an the lateral faces are rectangles
Acute Triangle
A triangle with three acute angles.
Octagonal prism
16 vertices 24 edges
hexagonal prism
A prism with Hexagonal (six sided) bases
cube
A prism with six square faces
rectangular prism
A solid shape that has: 6 faces (4 rectangles & 2 squares), 8 vertices (corners), and 12 equal edges.
Sphere
A solid shape that is perfectly round like a ball. No faces, edges, or vertices.
Square pyramid
A three dimensional shape with a square base, 4 triangular faces, and one vertex at the top
Isosceles Triangle
A triangle with at least two congruent sides.
Scalene Triangle
A triangle with no congruent sides.
Obtuse Triangle
A triangle with one obtuse angle.
Right Triangle
A triangle with one right angle.
Multiplier = 180 / (1 + 2 + 3) = 180 / 6 = 30 Smallest Angle = 1(30) = 30 degrees Largest Angle = 3(30) = 90 degrees
The ratio of the measures of three angles of a triangle is 1:2:3. Find the measures of the smallest and largest angles.
Multiplier = 180 / (1 + 4 + 7) = 180 / 12 = 15 Smallest Angle = 1(15) = 15 degrees Largest Angle = 7(15) = 105 degrees
The ratio of the measures of three angles of a triangle is 1:4:7. Find the measures of the smallest and largest angles.
Multiplier = 180 / (2 + 3 + 4) = 180 / 9 = 20 Smallest Angle = 2(20) = 40 degrees Largest Angle = 4(20) = 80 degrees
The ratio of the measures of three angles of a triangle is 2:3:4. Find the measures of the smallest and largest angles.
x = 7 (Set any two sides equal to each other>)
The triangle is equilateral. Find x.
Remote Interior Angle
The two nonadjacent interior angles corresponding to each exterior angle of a triangle.
2x + (5x + 3) + (5x + 3) = 180 12x + 6 = 180 12x = 174 x = 14.5
The vertex angle of an isosceles triangle measures (2x) degrees, and one of the base angles measures (5x + 3) degrees. Find x.
2x + 50 + 50 = 180 2x + 100 = 180 2x = 80 x = 40
The vertex angle of an isosceles triangle measures (2x) degrees, and one of the base angles measures 50 degrees. Find x.
5x + 5x + 40 = 180 x = 14
The vertex angle of an isosceles triangle measures 40 degrees, and one of the base angles measures (5x) degrees. Find x.
Cone
Triangle shaped top with a round cylinder at the bottom.
Triangular prism
Triangular bases. 5 faces, 9 edges, and 6 vertices.
True
True or False. Every equilateral triangle is also isosceles.
False
True or False. Every isosceles triangle is also equilateral.
Congruent Triangles
Two triangles whose corresponding sides and angles are congruent.