Chapter 5 1st Quiz Flashcards
Scalene
No congruent sides
Isosceles
At least 2 congruent sides
Equilateral
All sides congruent
Acute
3 acute angles
Obtuse
1 obtuse angle
Right
1 right angle
Equiangular
All angles congruent
Equilateral is _____ isoceles
Always
Isosceles is ______ equilateral
Sometimes
△ΣT (Triangle Sum Theorem)
Sum measures of interior angles of a triangle is equal to 180 degrees
Exterior Angle Theorem (EAT)
The measure of exterior angles of a triangle is equal to the sum measure of two remote interior angles
Right Triangle Corollary
Acute angles of right triangles are complementary
How do you prove triangles are congruent?
Use the definition of congruent triangles.
Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then third angles are also congruent.
Side-Angle-Side Theorem (SAS)
Official Definition
If two sides and included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
SAS My Definition
If two triangles have equal two sides and one angle attached to the sides, then the triangles are congruent.
SAS (remember this)
The angle has to be where the two known sides come together.
Base Angle Theorem (BAT)
Official Definition
If two sides of triangles are congruent, then the angles opposite those sides are congruent.
Converse Base Angle Theorem (CBAT)
Official Definition
If two angles of triangles are congruent, then the sides opposite are congruent.
BAT
My definition
If two sides of a triangle are congruent, the angles opposite those sides are congruent.
CBAT
My definition
If two angles of a triangle are congruent, the sides coming from those angles are congruent.
Equilateral Triangle Corollaries
1) If a triangle is equal then equiangular
2) If a triangle is equiangular then equal
3) An equiangular triangular has 3 60 degree angles
***CPCTC
Corresponding parts of congruent triangles congruent
The three things not named as congruent while using SAS can be shown as congruent
*Must use SAS to use CPCTC
*To use CPCTC you must know that the two triangles are congruent
Solve for x and y using the sum of a triangle
The measures of a triangle equal 180 degrees. Use angle measures to solve as an equation.
Solve for x and y using exterior angles
The opposite angles of a triangle equal the exterior angle of a triangle.
Definition of the midpoint of a circle
All lines coming from the midpoint of a circle are congruent.
