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Problem Set B, continued 24 Given: PÝ bisects ZVPZ. (2x + 7)°, LVPY ZZPY = (3x - 9)°, PZ = ¹/x + 5, PV = x - 3 Prove: AVPY= AZPY (Use a paragraph proof.) 25 Given: 23 = 41, 44 = 42, ZDAC = 23, ZBAC = 21, AD AB Prove: ACAD= ACAB Problem Set C 26 Given: AB = AE; Z A D P 3 4 (1-x2107) A 1/2 E 2x+7 D

Problem Set B, continued 24 Given: PÝ bisects ZVPZ. (2x + 7)°, LVPY ZZPY = (3x - 9)°, PZ = ¹/x + 5, PV = x - 3 Prove: AVPY= AZPY (Use a paragraph proof.) 25 Given: 23 = 41, 44 = 42, ZDAC = 23, ZBAC = 21, AD AB Prove: ACAD= ACAB Problem Set C 26 Given: AB = AE; Z A D P 3 4 (1-x2107) A 1/2 E 2x+7 D

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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How to do proof #25

**Problem Set B, continued** **24. Given:** - \( \overrightarrow{PY} \) bisects \(\angle VPZ\). - \(\angle WPY = (2x + 7)^\circ\). - \(\angle ZPY = (3x - 9)^\circ\). - \(PZ = \frac{1}{2}x + 5\). - \(PV = x - 3\). **Prove: \(\triangle VPY \cong \triangle ZPY\)** (Use a paragraph proof.) *Diagram:* A triangle with point \(P\) at the top, \(V\) on the left, and \(Z\) on the right. The line \(PY\) bisects \(\angle VPZ\). --- **25. Given:** - \(\angle 3 \cong \angle 1\), - \(\angle 4 \cong \angle 2\), - \(\angle DAC \cong \angle 3\), - \(\angle BAC \cong \angle 1\), - \(AD \cong AB\). **Prove:** \(\triangle CAD \cong \triangle CAB\) *Diagram:* A quadrilateral divided into triangles by diagonals, with points labeled. Angles and sides are marked to illustrate congruence. --- **Problem Set C** **26. Given:** - \(\overline{AB} \cong \overline{AE}\), - \(\overrightarrow{AE}\) and \(AC\) trisect \(\angle BAD\), - \(AB \perp BC\), - \(AE \perp DE\). **Conclusion:** \(\triangle ABC \cong \triangle AED\) *Diagram:* A geometric shape with points \(A\), \(B\), \(C\), \(D\), and \(E\), displaying trisection and perpendicularity of lines and angles.
Transcribed Image Text:**Problem Set B, continued** **24. Given:** - \( \overrightarrow{PY} \) bisects \(\angle VPZ\). - \(\angle WPY = (2x + 7)^\circ\). - \(\angle ZPY = (3x - 9)^\circ\). - \(PZ = \frac{1}{2}x + 5\). - \(PV = x - 3\). **Prove: \(\triangle VPY \cong \triangle ZPY\)** (Use a paragraph proof.) *Diagram:* A triangle with point \(P\) at the top, \(V\) on the left, and \(Z\) on the right. The line \(PY\) bisects \(\angle VPZ\). --- **25. Given:** - \(\angle 3 \cong \angle 1\), - \(\angle 4 \cong \angle 2\), - \(\angle DAC \cong \angle 3\), - \(\angle BAC \cong \angle 1\), - \(AD \cong AB\). **Prove:** \(\triangle CAD \cong \triangle CAB\) *Diagram:* A quadrilateral divided into triangles by diagonals, with points labeled. Angles and sides are marked to illustrate congruence. --- **Problem Set C** **26. Given:** - \(\overline{AB} \cong \overline{AE}\), - \(\overrightarrow{AE}\) and \(AC\) trisect \(\angle BAD\), - \(AB \perp BC\), - \(AE \perp DE\). **Conclusion:** \(\triangle ABC \cong \triangle AED\) *Diagram:* A geometric shape with points \(A\), \(B\), \(C\), \(D\), and \(E\), displaying trisection and perpendicularity of lines and angles.
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