Angle Relationships
What are adjacent angles? Give an example.
Two angles that share a common side and vertex.
Name the three types of triangles by sides.
Equilateral, isosceles, and scalene.
Name 3 triangle congruence postulates.
SSS, SAS, ASA, AAS, HL.
What is a centroid and how is it found?
The point where the medians intersect.
What is a polygon?
A closed figure made of straight lines.
What are vertical angles? Are they always congruent?
Angles opposite each other when two lines intersect; they are always congruent.
Name three types of triangles by angles.
Acute, Obtuse, Right
What is needed to prove triangles congruent by ASA?
Two angles and the included side are congruent.
What is an incenter?
The point where the angle bisectors intersect; equidistant from the triangle's sides
Define a regular polygon.
A polygon that is both equilateral and equiangular.
Define complementary vs. supplementary angles.
One pair sums to 90°, the other sums to 180°.
What does the triangle inequality theorem say?
The sum of the lengths of any two sides must be greater than the third side.
What is the HL Theorem and when can it be used?
Used for right triangles when a leg and hypotenuse are congruent.
What is a circumcenter?
The point where the perpendicular bisectors intersect; equidistant from the vertices
What’s the formula for the interior angles of a polygon?
(n-2) times 180
What are alternate interior angles, and when are they congruent?
Angles that lie inside two lines and are on opposite sides of the transversal.
What is special about the angles in an equilateral triangle?
All three angles are 60 degrees.
Define “median” and explain how it’s used in a proof.
A segment from a vertex to the midpoint of the opposite side.
What is an orthocenter?
The intersection of the altitudes of a triangle.
What’s the formula for the exterior angles of a polygon?
The sum of exterior angles is always 360°, no matter how many sides.
Name all 8 angle pairs formed by a transversal cutting parallel lines.
Corresponding, alternate interior, alternate exterior, same-side interior, vertical, adjacent, linear pair, and supplementary angles.
In a right triangle, what kind of angle is opposite the hypotenuse?
A right angle.
Given: AB ≅ DE, BC ≅ EF, angle ABC and angle DEF are right. Prove these two triangles are congruent.
Triangles are congruent by the HL theorem.
What’s the 2:1 property of the centroid in a triangle?
The centroid divides each median into a 2:1 ratio from vertex to midpoint.
List 3 properties of parallelograms.
Opposite sides are parallel, opposite angles are congruent, and diagonals bisect each other.