Triangle Unit Flashcards
How do you name a triangle?
With the symbol for triangle (∆) and the 3 vertices in any order
What do we call a triangle with no sides congruent?
Scalene
What do we call a triangle with 2 congruent sides?
Isosceles
What do we call a triangle with all 3 sides congruent?
Equilateral
An equilateral triangle is automatically what?
Equiangular
What does equiangular mean?
All the angles are congruent
What do we know about the angles in an equilateral triangle?
All have measure 60º
What do we know about the angles in an isosceles triangle?
Base angles are congruent
The angle measures in any triangle add up to what?
180º
What are the classifications of triangles based on its angles?
Acute, right, obtuse
Define obtuse triangle.
A triangle with an obtuse angle
Define right triangle.
A triangle with a right angle
Define acute triangle.
A triangle with all acute angles
The acute angles in a right triangle are what?
Complementary
How do you draw an exterior angle?
Extend one side of the triangle. The angle is made by the extension and side of the triangle
The measure of the exterior angle is the same as what?
The sum of the measures of the remote interior angles
What is a median of a triangle?
A line segment from the vertex to the midpoint of the opposite side
What should you mark whenever you have a median?
Congruent segments
What is an altitude of a triangle?
A line segment from a vertex that is perpendicular to the opposite side
What should you mark whenever you have an altitude?
Right angles
What is special about the altitudes in a right triangle?
The 2 legs are also altitudes
What is special about the altitudes in an obtuse triangle?
The 2 altitudes from the acute angles go outside the triangle
What is special about the altitude from the vertex angle in an isosceles triangle?
It is also a median and angle bisector
What is special about the altitudes in an equilateral triangle?
They are all also medians and angle bisectors
Define a midsegment of a triangle.
A line segment connecting the midpoints of 2 sides of the triangle
What are the two properties for a midsegment of a triangle?
It is parallel to the 3rd side and half the length of the 3rd side
What should you mark when you have a midsegment?
Parallel lines, congruent corresponding angles from the parallel lines, congruent segments from the midpoints
What is the definition of two congruent triangles?
Two triangles with all the corresponding sides congruent and all the corresponding angles congruent
What are the methods to prove any 2 triangles congruent?
SSS, SAS, ASA, AAS
What are the extra methods to prove two right triangles congruent?
LL, LA, HA, HL
Which of the four methods of proving right triangles congruent is most important, and why?
HL because it is the only method that does not correspond to one of the methods that can prove ALL triangles congruent
What does CPCTC mean?
Corresponding Parts of Congruent Triangles are Congruent
In a triangle, which angle must be the largest?
The one opposite the largest side
In a triangle, which angle must be the smallest?
The one opposite the smallest side
In a triangle, which side must be the largest?
The one opposite the largest angle
In a triangle, which side must be the smallest?
The one opposite the smallest angle
The sum of the lengths of the smallest 2 sides of a triangle must be what?
Greater than the length of the 3rd side
If 2 sides of a triangle have lengths x and y, what are all the possible lengths for the 3rd side?
| x – y | < 3rd side < x + y
x – y | < 3rd side < x + y
