EOC Prep: Triangles.

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Presentation transcript:

EOC Prep: Triangles

Triangle Classification: Angles Right Triangle: A triangle with one right angle. Acute Angle: A triangle with three acute angles. Obtuse Angle: A triangle with one obtuse angle.

Triangle Classification: Sides Scalene Triangle: Triangle with no congruent sides. Isosceles Triangle: Triangle with two congruent sides and two congruent angles. Equilateral Triangle: Triangle with three congruent sides and angles.

The sum of the inside angles of every triangle is 180 The sum of the inside angles of every triangle is 180. If you know 2 angle measures you can find the third one.

Isosceles Triangles

Isosceles Triangle Conjecture If a triangle is isosceles, then its base angles are congruent.

Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then it is an isosceles triangle.

Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is greater than the lengths of the third side.

Relationship Between Sides & Angles in Triangles The largest angle is across from the longest side. The smallest angle is across from the shortest side. The medium angle is across from the mid-sized side.

Side Side Side SSS Congruence Conjecture: If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

Side Angle Side SAS Congruence Conjecture: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. **The angle must be adjacent to both sides!**

Angle Side Side Side Side Angle (SSA) SSA is NOT a triangle congruence shortcut. Counterexample:

Angle Side Angle Angle Side Angle (ASA) ASA Congruence Conjecture: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Side Angle Angle Side Angle Angle (SAA) SAA Congruence Conjecture: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

Angle Angle Angle NOOO! AAA is NOT a triangle congruence shortcut. Counterexamples:

Good Bad SSS SSA SAS AAA ASA SAA

Corresponding parts of congruent triangles are congruent. CPCTC