Triangles are classified in two different ways. These ways are?
What is by their angles and by their sides.
100
The interior angle theorem for triangles states?
The sum of the interior angles of a triangle is equal to 180 degrees.
100
How many medians are there in each triangle and where do they meet?
What is 3 medians, and they meet at a point of concurrency inside the triangle called the Centroid.
100
What are angle bisectors and where do their endpoints lie?
They are segments that cut an angle in half with one endpoint of the segment starting at the vertex of each angle of a triangle and the other on the side opposite that vertex.
100
In the figure, state the angles from largest to smallest.
Angles:
200
The three ways you can classify triangles based on their sides. These are?
What is and equilateral triangle, isosceles triangle and scalene triangle.
200
What does the exterior angle theorem for triangles state?
The measures of an exterior angle is a triangle is equal to the sum of the measures of the two remote interior angles.
200
The orthocenter and altitudes of a triangle can lie where for an acute, obtuse and right triangle?
Acute:
Altitudes:the interior of a triangle
Orthocenter: the interior of a triangle
Obtuse:
Altitudes: the interior/exterior of a triangle
Orthocenter: The exterior of a triangle
Right:
Altitudes: the interior/on the side of a triangle
Orthocenter: On the tringle
200
What are the names of the points of concurrence for angle bisectors and perpendicular bisectors?
What is a incenter (Angle bisector) and a circumcenter (Perpendicular bisector)
200
State if the three numbers can be the measures of the sides of a triangle. 12, 14, 7
YES
300
There are four ways to classify a triangle based on their angles. These are?
What is an acute triangle, an equiangular triangle, and obtuse triangle and a right triangle.
300
Acute angles of a right triangle are?
Complementary
300
The figure shows a triangle with one of its medians (segment CJ). Find the value of x.
What is x = 10.
300
In the figure, segment UP is an angle bisector, what is the value of x?
What is x=7
300
Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 11, 6
What is 5 < x < 17
400
Explain the all 7 types of ways to classify triangles.
What is:
Acute Triangle - has 3 acute angles (each less than 90 degrees)
Obtuse Triangle - has 1 obtuse angle (between 90 < x < 180 degrees)
Right Triangle - has 1 right angle (angle equals 90 degrees)
Equiangular Triangle - 3 congruent angles (all equal to 60 degrees)
Equilateral Triangle - 3 congruent sides
Isosceles Triangle - at least 2 congruent sides
Scalene Triangle - no congruent sides
400
Find the value of x and the measure of angle A in the given figure.
x = -6
angle A = 44 degrees
400
Given the following coordinates, A(-1, 11), B(3, 1), and C(7, 6) find the coordinates of the orthocenter of the triangle.
What is (3, 6)
400
In the figure, segment FP is an angle bisector, what is the measure of angle 2?
What is the measure of angle 2 = 20 degrees
400
Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 8, 10
What is 2 < x < 18
500
In Triangle ABC, angle A and angle B are congruent. What do you know about this triangle, what is the value of x, and what is the measure of segment AC
What is an Isosceles Triangle, x = 11 and AC = 29
500
Find the measure of the angle indicated in the following image.
The measure of angle H = 52 degrees
500
In the figure a triangle is given with one or more of its medians. Calculate the measure of segment MN.
What is segment MN = 14
500
Given the coordinates of the triangle ABC, A(3, 7), B(13, 5), C(6, 2), what is the slope of the perpendicular bisector of segment AB?
What is m = 5/1 or 5
500
Two sides of a triangle have the following measures. Find the range of possible measures for the third side. (2x+22), (5x-7), and (x+7)