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Below is a two-column proof incorrectly proving that the three angles of ΔPQR add up to 180°: Statements Reasons Draw line ZY parallel to segment PQ; Construction m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY; Angle Addition Postulate ∠ZRP ≅ ∠RPQ; Alternate Interior Angles Theorem ∠QRY ≅ ∠PQR; Alternate Interior Angles Theorem
Alternate Interior Angles Theorem, Converse of Corresponding Angles Postulate, Given, Reflexive Property, Transitive Property, Vertical Angles Theorem Statement Reasons Transversal t cuts line l and line m. 1. Given ∠2 ≅ ∠7 2. ∠2 ≅ ∠3 3. ∠3 ≅ ∠7 4. l ║m 5.
Now, the converse alternate interior angles theorem states that if two lines are intersected by a transversal and the alternate interior angles are congruent, then the lines are parallel. In the context of the proof, the missing reason is the converse alternate interior angles theorem.
2. m∠AGE ≅ m∠HGB (Vertical Angles Theorem) 3. m∠HGB ≅ m∠CHE (Alternate Interior Angles Theorem) 4. m∠AGE ≅ m∠CHE (Transitive Property) The missing justification in step 4 is the Transitive Property, which states that if two angles are congruent to a third angle, then they are congruent to each other.
In the given figure Lines NM & PO are parallel .From statement 2 and 3 we have <2=<3 and <1=<3. The Transitive property states: If two sides or angles are equal to one another and one of them is equal to third side or angle then the first side or angle is equal to the third angle or side .The formula for this property is if a = b and b = c, then a = c.
The paragraph proof offers proof for the Same-Side Interior Angles Theorem. The proof establishes the congruence of ∠JNL and ∠HMN by demonstrating their angle measures are equal. It utilizes the Same-Side Interior Angles Theorem, stating that if two parallel lines are intersected by a transversal, then same-side interior angles are ...
The missing step in the proof is the one that justifies that ∠21 ≅ ∠24, and ∠23 ≅ ∠25 are pairs of supplementary angles. This step is required in order to apply the Alternate Interior Angles Theorem, which is mentioned in the proof. We need to confirm that the lines in question are indeed parallel, as this is a necessary condition ...
Match the following reasons with the statements given. Complete the proof for the theorem 4-18 mentioned above. 1. DO = OB, AO = OC If two sides = and ||, then a parallelogram. 2. DOC = AOB Vertical angles are equal. 3. Triangle COD congruent to Triangle AOB CPCTE 4. 1 = 2, AB = DC Given 5. AB||DC If alternate interior angles =, then lines ...
The given paragraph offers a proof for the Alternate Interior Angles Theorem. The Alternate Interior Angles Theorem states that if two parallel lines are intersected by a transversal, then the pairs of alternate interior angles are congruent. Let's analyze the paragraph: 1. Given Information: - Lines WZ and XY intersect at point V. 2.
Use the drop-down menus to complete the paragraph proof. we are given that xy is parallel to zw. if xz is a transversal that intercepts xy and zw, angle and angle are alternate interior angles. since xy is parallel to zw, we know that these angles are . we also know that angle xvy and angle zvw are angles, and thus congruent. we can conclude that xyv ~ zwv using the similarity theorem.