With all vectors being at right angles to one another, their addition leads to a resultant that is at the hypotenuse of a right triangle. The Pythagorean theorem can then be used to determine the magnitude of the resultant. To see how this process works with an actual vector addition problem, consider Example 3 shown below. Example 3: Triangle Congruence Worksheet #2 I. For each pair of triangles, tell which postulate, if any, can be used to prove the triangles congruent. 1. 3. 5. ARTS= 7. ADEC ABEC ACBA ABCP 2. ACDE= 6. AABC= 8. ASAT = AABF ACDF AADC ASAR Given: ñÛbisectsZABC A) Triangle Sum Theorem B) Definition of a right angle C) Definition of congruent angles D) Linear Pair Theorem E) Definition of complementary angles 49. Choose from: A) Triangle Sum Theorem B) Definition of a right angle C) Definition of congruent angles D) Linear Pair Theorem E) Definition of complementary angles 50. Choose from: A) Triangle ...

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Classifying Triangles by Angles . Acute – 3 acute angles . Right – 1 right angle . Obtuse – 1 obtuse angle . Equiangular – 3 congruent angles . Theorem 4.1 – Triangle Sum Theorem . The sum of the measures of the interior angles of a triangle is 180°. Theorem 4.2 – Exterior Angle Theorem . The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent angles.**Annotation js**

**AMNP is a right triangle. L M is a right angle and mLN is 58. Find Reasoning Explain why this statement must be true: If a triangle is a right triangle, its acute angles are complementary. 1 EXAMPLE Find mL1. Applying the Triangle Angle-Sum Theorem 350 650. Draw and mark a triangle to fit each description. If no triangle can be drawn, write not possible and explain why. c. obtuse equiangular a. acute scalene b. isosceles right 3 EXAMPLE Classifying a Triangle Classify the triangle by its ... the point of intersection of the of the triangle. The Centroid Theorem states that the centroid of a triangle is located of the distance from each vertex to the of the opposite side. SP 2__ 3 Centroid Theorem SP 2__ (3) Substitute the known value for SB. SP Simplify. B.RA RP __2 3 Centroid Theorem 2__ (3) Substitute known values for RP. **

**3. ∠ABD ∠BDC 4. −−− BD −−− BD 5. ABD CDB 1. Given 2. Given 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence 5. ASA 4-5 ASA Postulate 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. Example ... 3. ∡DBA ∡ECA 3. Substitution Property 5. ∡DBA supp ∡3; ∡ECA supp ∡4 5. Linear Pair Theorem 6. ∡3 ∡4 6. Congruent Supplements Theorem 7. ̅̅̅̅ ̅̅̅̅ 7. 8. ABC is isosceles 8. If the legs of a triangle are congruent, then triangle is isosceles. A right triangle is a triangle that has one 90° angle, which is often marked with a symbol. Properties of Similar Triangles If two triangles are similar, then their corresponding angle measures are equal and their corresponding side lengths have the same ratio. **

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