Angles & Sums
According to the Triangle Sum Theorem, all interior angles of a triangle must add up to this many degrees.
What is 180
These are the three main theorems used to prove two triangles are similar
What are AA~, SAS~, and SSS~
This famous theorem states a2+b2=c2.
What is the Pythagorean Theorem
This segment connects the midpoints of two sides and is always parallel to and half the length of the third side
What is a Midsegment
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be this in relation to the third side
What is greater than the third side
This theorem states that the measure of an exterior angle is equal to the sum of the two remote (opposite) interior angles
What is the Exterior Angle Theorem
This congruence shortcut is "illegal" and cannot be used to prove triangles are congruent, unless it is a right triangle
What is SSA
In a right triangle, this is the name of the longest side, located across from the 90∘ angle
What is the hypotenuse
This is the point where the three medians of a triangle intersect
What is the Centroid?
If a triangle has side lengths of 4, 5, and x, x cannot be this number because 4+5 is not greater than it.
What is 9
In an isosceles triangle, if the vertex angle is 40∘, these are the measures of the two base angles
What are 70∘ and 70∘?
If two triangles are proven congruent by this theorem, it means three sides of one are equal to three sides of the other
What is SSS
If a right triangle has legs of 5 and 12, this is the length of the hypotenuse.
What is 13?
The Centroid divides a median into two segments with this specific ratio
What is 2:1 or 2/3 of the way from the vertex
In any triangle, the largest angle is always located across from this side
What is the longest side?
This is the measure of each interior angle in an equilateral triangle.
What is 60∘
This acronym stands for the rule that once triangles are proven congruent, all their remaining matching parts are also congruent
What is Corresponding Parts of Congruent Triangles are Congruent
In a 45∘−45∘−90∘ triangle, if the legs are length x, the hypotenuse is this.
What is x2
This segment is drawn from a vertex perpendicular to the opposite side.
What is the Altitude
This property states that a shared side or angle is congruent to itself (e.g., AB≅AB).
What is the Reflexive Property?
If a triangle has interior angles of x, 2x, and 3x, this is the value of x.
What is 30? (x+2x+3x=180→6x=180)
similar triangles, while the angles remain congruent, the side lengths are not equal but are instead this.
What is proportional?
Using the Converse of the Pythagorean Theorem, if a2+b2<c2, the triangle is classified as this.
What is obtuse
The three perpendicular bisectors of a triangle meet at this point, which is equidistant from all vertices.
What is the Circumcenter
Given a triangle with sides 7 and 10, this is the range of possible values for the third side x
What is 3<x<17