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AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent 4. AC ≅ AC 4. reflexive property 5. CAD ≅ ACB 5.
By applying the linear pairs theorem to the figure, we can logically deduce the following supplementary angles: m∠ZRY = 180° (Definition of supplementary angles). In conclusion, the sum of the three interior angles subtended by triangle PQR equals angle ZRY (180°) based on the definition of supplementary angles.
AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent 4. AC ≅ AC 4. reflexive property 5. CAD ≅ ACB 5.
Given that AB ∥ DE and using definitions of vertical angles and alternate interior angles, we can conclude that ABC and EDC are similar triangles. Explanation: To prove that ABC ~ EDC, we need to show that their corresponding angles are congruent.
3. ∠1 = ∠2 Vertically opposite angles formed by two intersecting lines are equal. 4. BC ║ AD By definition, the opposite sides of a parallelogram are parallel. 5. ∠3 = ∠4 Based on the property of equality of the alternate interior angles of two parallel lines . 6. Triangle BET congruent to Triangle DFT by Angle-Side-Angle rule of ...
Given: ad ≅ bc and ad ‚à• bc, prove that abcd is a parallelogram. Statements Reasons 1. ad ≅ bc; ad ‚à• bc 1. given 2. ∠cad and ∠acb are alternate interior ∠s 2. definition of alternate interior angles 3. ∠cad ≅ ∠acb 3. alternate interior angles are ≅ ac 4. reflexive property 5. cad ≅ abc 5.
→AD║BC→ Definition of a Parallelogram. ⇒∠CAD ≅ ∠ACB →→[Alternate interior angles theorem] ⇒Line segment BC ≅ Line segment DA→→Definition of a Parallelogram. In Δ A DE and Δ C BE. AD=BC⇒Proved above. ∠CAD=∠ACB ⇒Alternate interior angles theorem. ∠ADB=∠CBE ⇒Alternate interior angles theorem
The alternate interior angles theorem states that the alternate interior angle formed by the two parallel lines and their shared transversal are congruent. Definition of congruent angles Congruent angles are angles that have the same measure.
∠CAD ≅ ∠ACB Alternate interior angles theorem Definition of a Parallelogram ∠ADB ≅ ∠CBD Alternate interior angles theorem ΔADE ≅ ΔCBE Angle-Side-Angle (ASA) Postulate Line segment BE is congruent to line segment DE CPCTC Line segment AE is congruent to line segment CE CPCTC Line segment AC bisects Line segment BD Definition of a ...
a. corresponding angels theorem b. alternate interior angels theorem c. vertical angels theorem. d. alternate exterior angels theorem Therefore, m∠1 = m ∠5 by the definition of congruent. We also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the _____. a.