?Draw and label a figure for each conjecture. Then write a paragraph proof.In

List three things that can be used to justify a statement in a paragraph proof.

Explain how deductive reasoning is used in paragraph proofs.

Write a paragraph proof for each conjecture. If \(T\) bisects \(\overline{P N}\) and \(\overline{R M}\), then \(\angle M \cong \angle R\). Plan: Use a triangle congruence postulate. Equation Transcription: ? Text Transcription: T overline PN overline RM angle M approx equal to angle R

If \(p\) and \(q\) are cut by transversal \(t\), and \(\angle 1\) is supplementary to \(\angle 2\), then \(p \ \| \ q\). Equation Transcription: ? Text Transcription: p q t angle 1 angle 2 p parallel to q

A carpenter is building a flight of stairs. The tops of the steps are parallel to the floor, and the bottom of the stringer makes a \(25^{\circ}\) angle with the floor. Prove that the top of the steps makes a \(25^{\circ}\) angle with the top of the stringer. Equation Transcription: Text Transcription: 25^circ

Write a paragraph proof for each conjecture. If \(\angle D \cong \angle T\) and \(M\) is the midpoint of \(\overline{D T}\), then \(\Delta D E M \cong \Delta T E M\). Plan: Use a triangle congruence postulate. Equation Transcription: ? ? Text Transcription: angle D approx equal to angle T M overline DT Delta DEM approx equal to Delta TEM

Write a paragraph proof for each conjecture. If \(\overline{M Q} \| \overline{N P}\) and \(m \angle 4=m \angle 3\), then \(m \angle 1=m \angle 5\). Plan: Use corresponding angles and alternate interior angles. Equation Transcription: ? Text Transcription: overline MQ parallel to overline NP m angle 4 = m angle 3 m angle 1 = m angle 5

If \(\angle 3 \cong \angle 4\), then \(\overline{M A} \cong \overline{M C}\). Equation Transcription: ? ? Text Transcription: angle 3 approx equal to angle 4 overline MA approx equal to overline MC

If \(\Delta G M K\) is an isosceles triangle with vertex \(\angle G M K\) and \(\angle 1 \cong \angle 6\), then \(\Delta G M H \cong \Delta K M J\). Equation Transcription: ? ? Text Transcription: Delta GMK angle GMK angle 1 approx equal to angle 6 Delta GMH approx equal to Delta KMJ

If \(\overline{P H}\) bisects \(\angle Y H X\) and \(\overline{H P} \perp \overline{Y X}\), then \(\Delta Y H X\) is an isosceles triangle. Equation Transcription: Text Transcription: overline PH angle YHX overline HP perpendicular overline YX Delta YHX

If \(\angle 5 \cong \angle 6\) and \(\overline{F R} \cong \overline{G S}\), then \(\angle 4 \cong \angle 3\). Equation Transcription: ? ? ? Text Transcription: angle 5 approx equal to angle 6 overline FR approx equal to overline GS angle 4 approx equal to angle 3

Draw and label a figure for each conjecture. Then write a paragraph proof. In quadrilateral \(E F G H\), if \(\overline{E F} \cong \overline{G H}\) and \(\overline{E H} \cong \overline{G F}\), then \(\Delta E F H \cong \Delta G H F\). Equation Transcription: ? ? ? Text Transcription: EFGH overline EF approx equal to overline GH overline EH approx equal to overline GF Delta EFH approx equal to Delta GHF

Draw and label a figure for each conjecture. Then write a paragraph proof. If an angle bisector of a triangle is also an altitude, then the triangle is isosceles.

Draw and label a figure for each conjecture. Then write a paragraph proof. The medians drawn to the congruent sides of an isosceles triangle are congruent.

When a prosecuting attorney presents a closing argument in a trial, he or she gives a summary of the trial. Explain how the closing argument is like a paragraph proof.

Abby needs to divide a rectangular piece of fabric into three strips, each having the same width. The width of the fabric is \(10.5\) inches. Instead of dividing \(10.5\) by \(3\), Abby angles her ruler as shown in the figure, divides \(12\) by \(3\), and makes marks at \(4\) inches and \(8\) inches. Explain why this method divides the fabric into three strips having the same width. Equation Transcription: Text Transcription: 10.5 3 12 4 8

What conclusion can you draw about the sum of \(m \angle 1\) and \(m \angle 4\) if \(m \angle 1=m \angle 2\) and \(m \angle 3=m \angle 4\)? Equation Transcription: Text Transcription: m angle 1 m angle 4 m angle 1 = m angle 2 m angle 3 = m angle 4

If two lines are perpendicular, then they form four right angles. Lines \(\ell\) and \(m\) are perpendicular. What conclusion can you derive from these statements? \(\text { (Lesson 15-2) }\) Equation Transcription: ? Text Transcription: l m (Lesson 15–2)

Construct a truth table for each compound statement. \(\text { (Lesson 15-1) }\) \(\sim p \wedge \sim q\) Equation Transcription: Text Transcription: (Lesson 15–1) tilde p wedge tilde q

Construct a truth table for each compound statement. \(\text { (Lesson 15-1) }\) \(\sim q \rightarrow \sim p\) Equation Transcription: Text Transcription: (Lesson 15–1) tilde q right arrow tilde p

Construct a truth table for each compound statement. \(\text { (Lesson 15-1) }\) \(p \vee \sim q\) Equation Transcription: Text Transcription: (Lesson 15–1) p vee tilde q

Simplify \(\sqrt{8} \cdot \sqrt{9}\). \(\text { (Lesson 13-1) }\) Equation Transcription: Text Transcription: sqrt 8 cdot sqrt 9 (Lesson 13–1)

The median of a trapezoid is \(8\) meters. The height of the trapezoid is \(4\) meters. How is the area of this trapezoid changed when the median is doubled? \(\text { (Lesson 10-4) }\) a. The area is halved. b. The area is not changed. c. The area is doubled. d. The area is tripled. Equation Transcription: Text Transcription: 8 4 (Lesson 10–4)