Question

1. in parallelogram abcd, if ab = 2x + 3 and cd = 5x - 9, what is the value of x? a. x = 6 b. x = 4 c. x = 3 d. x = 5 23. what is the purpose of the given information in a geometric proof? a. to justify the proof b. to establish initial conditions or facts c. to list the steps needed to solve the proof d. to provide conclusions 24. what is the measure of an angle that intercepts a 100 - degree arc in a circle? a. 25 degrees b. 50 degrees c. 200 degrees d. 100 degrees

Explanation:

22.

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, \(AB = CD\). Given \(AB = 2x+3\) and \(CD = 5x - 9\), we set up the equation \(2x+3=5x - 9\).

Step2: Solve the equation for \(x\)

First, subtract \(2x\) from both sides: \(2x+3-2x=5x - 9-2x\), which simplifies to \(3 = 3x-9\). Then add 9 to both sides: \(3 + 9=3x-9 + 9\), giving \(12 = 3x\). Divide both sides by 3: \(\frac{12}{3}=\frac{3x}{3}\), so \(x = 4\).

In a geometric proof, the given information is used to establish the initial conditions or facts from which the proof is built.

The measure of an inscribed angle in a circle is half the measure of the intercepted arc. If the arc is 100 degrees, then the inscribed - angle is \(\frac{100}{2}=50\) degrees.

Answer:

b. \(x = 4\)

23.