Unit 5 Review State Standards 2: Write geometric proofs. 5: Prove triangles are congruent. 12: Find and use measures of sides and angles in triangles.

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Presentation transcript:

Unit 5 Review State Standards 2: Write geometric proofs. 5: Prove triangles are congruent. 12: Find and use measures of sides and angles in triangles. 13: Prove angle relationships. 16: Perform basic constructions. 17: Prove theorems by using coordinate geometry. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Classifying Triangles by sides Scalene: no congruent sides Isosceles: at least two congruent sides Equilateral: all three sides congruent by angles Acute: 3 acute angles Equiangular: all angles congruent (60 o ) Right: 1 right angle Obtuse: 1 obtuse angle

Theorems on Triangles Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 o. Exterior Angles Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Congruent Triangles definition all corresponding sides are congruent all corresponding angles are congruent postulates and theorems to prove congruent triangles

Using Congruent Triangles C.P.C.T.C. is used to indicate that the corresponding parts of already proven congruent triangles are congruent.

Isosceles and Equilateral Triangles The Base Angles Theorem, its converse, and its corollaries are used with Isosceles Triangles. The angles opposite the congruent sides of an isosceles triangle are congruent If two angles of a triangle are congruent, then the sides opposite the angles are congruent. A triangle is equilateral if and only if it is also equiangular.

Coordinate Proofs Coordinate proofs place figures on a coordinate plane and then use the distance formula, midpoint formula, slope formula, postulates, theorems, and definitions to prove assumptions.

Marker Boards Out!

Classify the triangle by its angles.

Classify the triangle by its sides

Classify the triangle by its angles and its sides.

Identify the hypotenuse of right triangle  BDC.

Identify the base of isosceles triangle  ABC.

Identify the legs of right triangle  ABD.

Find the measure of the numbered angle.

The variable expressions represent the angle measures of a triangle. Use the information to classify the triangle by its angles.

The variable expressions represent the angle measures of a triangle. Use the information to classify the triangle by its angles.

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

Which postulate or theorem can be used to prove the two triangles congruent?

D E F M N

D E M N

Statements Reasons

Find the missing coordinates without using any new variables.

P Q X Z Y R x y

Statements Reasons

Statements Reasons

(48, 48)