Logic Statements
Two or more points that lie on the same line.
What is collinear?
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
What are properties of isosceles triangles?
A transformation that preserves length and angle measure.
What is a rigid motion?
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
What is Side Side Side Theorem?
The angle bisectors of the angles of a triangle are concurrent at a point equidistance from the sides of the triangle.
What is an incenter?
An example that shows a statement or conjecture is false.
What is a counterexample?
The sum of the measures of all the angles of a triangle is 180.
What is the Triangle Angle-Sum Theorem?
A transformation that changes a coordinate point from (x,y) to (x,-y).
What is reflection across the x-axis?
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
What is Hypotenuse-Leg Theorem
A segment that has endpoints at a vertex and the midpoint of the side opposite the vertex.
What is a median?
This statement is obtained by negating and reversing both the hypothesis and the conclusion of a conditional.
What is the contrapositive?
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
What is Triangle Exterior Angle Theorem?
A transformation in a plane that maps all points of a preimage the same distance and in the same direction.
What is a translation?
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
What is Side Angle Side Congruence Criterion?
The balancing point of a triangle.
What is the centroid?
A law of logic that states if a conditional statement and its hypothesis are true, then the conclusion is also true.
What is the Law of Detachment?
The sum of the lengths of any two sides of a triangle is greater than the lengths of the third side.
What is Triangle Inequality Theorem?
A transformation that moves each point in the preimage around a point P by an angle measure of x*.
What is a rotation?
If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of another triangle, then the two triangles are congruent.
What is Angle Angle Side Congruency Criterion?
The point of concurrency of the lines containing the altitudes of a triangle.
What is an orthocenter?
A law of logic that states that given two true conditionals with the conclusion of the first being the hypothesis of the second, there exists a third true conditional having the hypothesis of the first and the conclusion of the second.
What is Law of Syllogism?
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.
What is the Hinge Theorem?
The composition of a reflection followed by a translation in a direction parallel to the line of reflection.
What is a glide reflection?
If two triangles are congruent, then each pair of corresponding sides is congruent and each pair of corresponding angles is congruent.
What is Corresponding Parts of Congruent Triangles are Congruent?
This point of concurrency is equidistant from each of the vertices.
What is a circumcenter?