Section 1 - Types of Triangles

Types of triangles pertaining to angles-

ACUTE TRIANGLE - when all angles in the triangle are less than 90 degrees

OBTUSE TRIANGLE - when one angle in the triangle measures more than 90 degrees

RIGHT TRIANGLE - When one angle in a triangle measures exactly 90 degrees

EQUIANGULAR TRIANGLE - When all angles in a triangle equal 60 degrees

PARTS OF A TRIANGLE -

BASE - side that is the 'bottom' of the triangle

LEG - any side that is not a base

VERTEX ANGLE - angle opposite the base

BASE ANGLES - two angles that touch the base

Types of triangles pertaining to sides -

SCALENE TRIANGLE - a triangle with no two sides of equal length

ISOSCELES TRIANGLE - a triangle with at least two sides that are congruent

EQUILATERAL TRIANGLE - a triangle with all sides congruent

PARTS OF A RIGHT TRIANGLE -

HYPOTENUSE - longest side of a right triangle, always opposite of the right angle

LEG - two sides that are not the hypotenuse

Theorems and postulates for triangles -

• The sum of all angles in a triangle is 180 degrees.
• If two angles in a triangles are congruent to two angles in another triangle, then the third angles are congruent.
• The acute angles of a right triangle are complementary.
• There can be at most, only one right or obtuse angle in a triangle.
• Congruence of triangles is reflexive, symmetric and transitive.
• An equilateral traingle is always equiangular.
• An equiangular triangle is always equilateral.
• Every angle in an equilateral triangle measures 60 degrees.
• If two angles in a triangle are congruent, the opposite sides are also congruent.
• If two sides in a triangle are congruent, the opposite angles are also congruent.

SSS - If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent

SAS - If two sides of and the included angle of one triangle are congurent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

AAS - If two angles and a non-included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

CPCTC - Corresponding Parts of Congruent Triangles are Congruent , once two triangles have been proven congruent, all parts of one triangle are congruent to the same parts on the other triangle.

Time to practice!

Classify each triangle by angles-

1)

2)

3)

4)

State whether each idea is always, sometimes, or never true -

8) The measures of the angles in a triangle always add up to 180 degrees.

9) A triangle can have two obtuse angles.

10) A right triangle has only one acute angle.

11) Given: triangle ABC = triangleDEF and AB = BC

Prove: triangle DEF is isosceles

Use these triangles for numbers 12 and 13.

12) Given: AB = DE , DF = AC and angle A = angle D

Prove: BC = EF

13) Given: triangle ABC = triangle DEF

Prove: angle A + angle B = angle D + angle E