Geometry 4 Flashcards
Triangle Sum Theorem
(4.1)- The sum of the measures of all the angles in a triangle will equal 180
How can you use the Triangle Sum Theorem and the Exterior Angle Sum Theorem
When finding out the measures of the angles in a triangles, especially when you are given two others
Exterior Angle Theorem
(4.2)- The measure of an exterior angle of a triangle is the sum to of the measures of the two remote interior angles
What is a Collary
A collary is a theorem directly proved by another
What are the Collieries of the Triangle Sum theorem
-The Acute angles of a right triangle are complementary
-There can be at most one obtuse angle in a triangle
Definition of congruent polygons (theres two)
-Two polygons are congruent if and only if a rigid transformation (or set of rigid transformations) maps one onto the other
-Two polygons are congruent if and only if all of their corresponding parts are congruent
In a right triangle, what is the relationship of the other two angles
They will add up to equal 90
How many obtuse angles can be in a triangle
One
4.3 Third Angles Theorem
If two out of three angles in two triangles are congruent then third angle is to
4.4 What are the properties of triangle congruence?
Reflexive, Symmetric, and Transitive
Which of SSS, SS, SAS, SA, AAA, and AA are necessary to find the other A and S
SSS and SAS
What are the most important steps to solving a geometry problem?
DRAW A PICTURE
ADD INFORMATION AS IT COMES
REMEMBER THEOREMS/POSTTULATEs
If angle A corresponds to angle C, the corresponding parts have to be written as AB=CD (T or F)
FALSE!
When using congruence it should be written as Ab is congruent to CD, but when you are just using distances it doesn’t matter!
What are the Triangle congruence theorems?
SSS, SAS, ASA, AAS
What are the right triangle congruence theorems?
LL, LH, LA, HA
Whats the difference between using a right angle congruence theorem and it’s matching triangle congruence theorem
The right triangle congruence theorems are like a short cut, you don’t need to mention that the right angles are congruent to use them.
What triangle has no equal sides, two equal sides, and three equal sides?
Scalene, isosceles, equilateral
What are the angle measures of an equilateral triangle?
60
Are the base angles in an isosceles triangle equal?
yes they are.
What are the properties of an equilateral triangle
The legs are congruent, the angle not opposite to either leg is the vertex, the angles that are opposite to the legs are the base angles
4.10 Isosceles triangle theorem
The base angles in an isosceles triangles are congruent
4.3 properties of an equilateral triangle
a triangle is equilateral if an only if its equal-angular
4.4 properties of an equilateral triangle
each angle of an equilateral triangle measures 60
