Question

solve for m∠edf. (this question is not multiple choice. show your work.) which of these statements is true? a.) ∠spq and ∠pqr are vertical angles. b.) ∠sop and ∠sor are vertical angles. c.) ∠poq and ∠ros are vertical angles. d.) ∠spo and ∠qro are vertical angles. which of these is not a method to determine triangle congruence? a.) sss b.) ssa c.) aas d.) sas e.) asa f.) hl which of these proves a and b are parallel? a.) corresponding angle postulate b.) corresponding angle postulate converse c.) alternate exterior theorem d.) alternate exterior theorem converse e.) line a and b arent parallel because 52 and 52 arent supplementary. solve for x ( this is not a multiple choice. show your work)

Explanation:

1. Solve for \(m\angle EDF\) (no figure - unable to solve without more info)

2. Which of these statements is true?

Step1: Recall vertical - angle definition

Vertical angles are formed by two intersecting lines and are opposite each other.

Step2: Analyze each option

In a quadrilateral \(SPQR\) with diagonals intersecting at \(O\), \(\angle POQ\) and \(\angle ROS\) are vertical angles because they are formed by the intersection of the diagonals \(SQ\) and \(RP\).

Step1: Recall triangle - congruence methods

The methods for triangle congruence are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles). SSA does not guarantee triangle congruence as it can result in two different triangles.

Step1: Identify the given angles

The two \(52^{\circ}\) angles are corresponding angles formed by a transversal intersecting lines \(a\) and \(b\).

Step2: Recall parallel - line postulates

The Corresponding Angle Postulate Converse states that if corresponding angles are congruent, then the lines are parallel.

Answer:

C. \(\angle POQ\) and \(\angle ROS\) are vertical angles.

3. Which of these is NOT a method to determine triangle congruence?