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25. In the figure shown, ZACD = ZACB and ZADC = ZABC. Prove that CD = CB. В D

25. In the figure shown, ZACD = ZACB and ZADC = ZABC. Prove that CD = CB. В 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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**Proofs** **25.** In the figure shown, \( \angle ACD \cong \angle ACB \) and \( \angle ADC \cong \angle ABC \). Prove that \( CD \cong CB \). *Diagram Description:* The diagram shows a quadrilateral \( ABCD \) with \( B \) and \( D \) at the top vertices. The angles \( \angle ACD \) and \( \angle ACB \) are congruent, and angles \( \angle ADC \) and \( \angle ABC \) are also congruent. You need to prove that the segments \( CD \) and \( CB \) are congruent. --- **26.** In isosceles \( \triangle ABC \) with \( \overline{AC} \cong \overline{AB} \), and \( \angle BDC \cong \angle CEB \), prove that \( BD \cong CE \). *Diagram Description:* The diagram shows an isosceles triangle \( \triangle ABC \) with \( A \) at the top vertex and a line intersecting the triangle at points \( D \) and \( E \). The angles \( \angle BDC \) and \( \angle CEB \) are marked congruent. You are to prove that segments \( BD \) and \( CE \) are congruent.
Transcribed Image Text:**Proofs** **25.** In the figure shown, \( \angle ACD \cong \angle ACB \) and \( \angle ADC \cong \angle ABC \). Prove that \( CD \cong CB \). *Diagram Description:* The diagram shows a quadrilateral \( ABCD \) with \( B \) and \( D \) at the top vertices. The angles \( \angle ACD \) and \( \angle ACB \) are congruent, and angles \( \angle ADC \) and \( \angle ABC \) are also congruent. You need to prove that the segments \( CD \) and \( CB \) are congruent. --- **26.** In isosceles \( \triangle ABC \) with \( \overline{AC} \cong \overline{AB} \), and \( \angle BDC \cong \angle CEB \), prove that \( BD \cong CE \). *Diagram Description:* The diagram shows an isosceles triangle \( \triangle ABC \) with \( A \) at the top vertex and a line intersecting the triangle at points \( D \) and \( E \). The angles \( \angle BDC \) and \( \angle CEB \) are marked congruent. You are to prove that segments \( BD \) and \( CE \) are congruent.
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