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 -
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-
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
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