Always Sometimes Never - triangles

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The triangle midline creates a triangle half the size of the original triangle.

...

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


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