Angles of Triangles
What is the sum of the interior angles of a triangle?
180 degrees
What does it mean for two triangles to be congruent?
They have the same shape and size
What is the first step in proving triangles are congruent?
Identify the corresponding parts (sides and angles) of the triangles
What is an isosceles triangle?
A triangle with at least two equal sides.
Solve for x.
x = 7
If one angle of a triangle is 50 degrees and another is 60 degrees, what is the measure of the third angle?
70 degrees
Name the four criteria for triangle congruence.
Side-Angle-Side (SAS), Side-Side-Side (SSS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS)
How do you prove triangles are congruent using the ASA criterion?
Show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
How are the angles of an equilateral triangle related to each other?
All angles are equal and measure 60 degrees each.
What theorem or postulate can be used to prove these two triangles congruent?
Side-side-side (SSS)
What are the names of the three types of triangles based on their angles?
Acute, right, and obtuse triangles
If two sides of one triangle are equal to two sides of another triangle, what can be said about their included angles?
The included angles are equal (SAS congruence)
What is a common reason for triangles to be congruent if they share a side?
If they share a side, it can be used in the SSS or SAS criteria for congruence.
If a triangle is isosceles, what can be said about the angles opposite the equal sides?
The angles opposite the equal sides are also equal.
What theorem or postulate can be used to prove these two triangles congruent?
Side-angle-side (SAS)
What is the relationship between the angles in a right triangle?
One angle measures 90 degrees, and the sum of the other two angles is 90 degrees.
Provide an example of two congruent triangles and explain how you can prove they are congruent.
Two triangles with sides of lengths 5, 12, and 13 can be proven congruent using the SSS criterion.
Describe how you can use the AAS criterion to prove two triangles are congruent.
Show that two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.
If two angles of an isosceles triangle measure 40 degrees each, what is the measure of the third angle?
100 degrees (180 - 40 - 40).
What is the triangle congruence statement?
triangle ABC = triangle DEF
Explain how the Exterior Angle Theorem works.
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles
What is the significance of the SSS criterion in proving triangle congruence?
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
If two triangles have two pairs of sides that are proportional and the included angles are equal, what can be concluded?
The triangles are similar, but additional information would be needed to prove they are congruent.
What is the relationship between the angles in an equilateral triangle?
All three angles are equal and 60 degrees.
Solve for the variables.
x = 20
y = 70