Always Sometimes Never - triangles
The triangle midline creates a triangle half the size of the original triangle.
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2 isosceles right triangles are similar.
always
2 isosceles triangles are similar if their base angles are congruent.
always
2 non-adjacent angles created by 2 intersecting lines are congruent.
always
2 triangles are congruent if 2 sides and the included angle of 1 are congruent to 2 sides and the included angle of the other.
always
2 triangles are congruent if 2 sides and the included angle of one are congruent to 2 sides and the included side angle of another.
always
2 triangles are similar if 2 angles of one triangle have the measures of 50 and 70 and 2 angles of the other triangle have the measures 60 and 50.
always
2 triangles are similar if 2 angles of one triangle have the same measure of 40 and 80 and 2 angles of the other triangle have measures of 60 and 80.
always
A median of a triangle bisects the opposite side.
always
A square is a rectangle.
always
An equiangular triangle is isosceles.
always
An obtuse triangle has exactly 1 obtuse angle.
always
If 2 angles are complementary they are each acute.
always
If 2 parallel lines are cut by a transversal the corresponding angles are congruent.
always
If 2 sides of a right triangle are congruent to the corresponding parts of another right triangle the triangles are congruent.
always
If a median of a triangle is also an altitude then it is an angle bisector too.
always
If an acute angle of one right triangle is congruent to an acute angle of another right triangle the triangles are similar.
always
If the corresponding sides of 2 similar triangles are in a ratio of 3:4 then the there perimeters are in a ratio of 3:4.
always
If the perimeters of 2 similar triangles are in a ratio 2:3 then the corresponding altitudes of those triangles are in a ratio 2:3.
always
The altitude to the base of an isosceles triangle is also an angle bisector.
always
The altitude to the base of an isosceles triangle is also the median to the base.
always
The bisectors of vertical angles are opposite rays.
always
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
always
The measure of an exterior angle of a triangle is larger than the measure of either remote interior angles.
always
The supplement of an acute angle is obtuse.
always
altitude of a triangle
an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
similar
having the same shape; having corresponding sides proportional and corresponding angles equal:
A median of a triangle does not contain the midpoint of the side to which it is drawn.
never
A right triangle is congruent to an obtuse triangle.
never
A right triangle is equilateral.
never
All 3 altitudes of a triangle fall outside the triangle.
never
An angle bisector of a scalene triangle divides the opposite side in a ratio of 1:1.
never
If 2 supplementary angles are congruent their complements are 45˚.
never
If a median of a triangle is also an altitude the the triangle is scalene.
never
One of the base angles of an isosceles triangle has a measure greater than that one of the exterior angles of the triangle.
never
The No Choice Theorem is a reason for stating 2 triangles are congruent.
never
The No Choice Thm is a reason for stating triangles are congruent.
never
The supplement of an acute angle is acute.
never
2 isosceles obtuse triangle are similar.
sometimes
2 isosceles triangles are similar if they have at least one pair of congruent angles.
sometimes
2 triangles are congruent if 2 sides and an angle of one are congruent to corresponding parts of another.
sometimes
A median of a triangle bisects the angle it is drawn from.
sometimes
A right triangle is scalene.
sometimes
A scalene triangle has 3 acute angles.
sometimes
An angle bisector of a scalene triangle divides the opposite sides in a ratio of 2:3.
sometimes
An exterior angle of a triangle is larger in measure than any angle of a triangle.
sometimes
An isosceles triangle is obtuse.
sometimes
Corresponding sides of similar triangles are congruent.
sometimes
If 2 angles are complementary and adjacent they are congruent.
sometimes
If 2 lines are cut by a transversal such that 2 interior angles on the same side of the transversal are congruent the lines are parallel.
sometimes
If <BAC is congruent to <ABC in triangle ABC then AB is congruent to BC.
sometimes
If AB congruent to BC in triangle ABC then angle BAC congruent to angle ABC.
sometimes
If an angle of 1 isosceles triangle is congruent to an angle of another isosceles triangle the triangles are similar.
sometimes
If angle TAB is congruent to angle TAC then TA is perpendicular to BC.
sometimes
In an angle of one isosceles triangle is congruent to an angle of another isosceles triangle the triangles are similar.
sometimes
The base of an isosceles triangle is shorter than either leg.
sometimes
The leg of an isosceles triangle is shorter than the the base.
sometimes
Vertical angles are complementary.
sometimes
Vertical angles are supplementary.
sometimes