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32. AABC is divided into two congruent triangles by BP. Fill in the blanks to show the congruent sides and angles. A а. АР ? b. ZAPB = ? c. ?= ZPCB d. APBA = ?

32. AABC is divided into two congruent triangles by BP. Fill in the blanks to show the congruent sides and angles. A а. АР ? b. ZAPB = ? c. ?= ZPCB d. APBA = ?

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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### Problem 32 **Given:** Triangle \( \triangle ABC \) is divided into two congruent triangles by line \( BP \). Fill in the blanks to show the congruent sides and angles. **Diagram:** The diagram shows triangle \( \triangle ABC \) with line \( BP \) dividing it into two smaller right triangles, \( \triangle ABP \) and \( \triangle BPC \). The right angle is marked at point \( P \). **Questions:** a. \( \overline{AP} \cong \) _____ b. \( \angle APB \cong \) _____ c. _____ \( \cong \angle PCB \) d. \( \triangle PBA \cong \) _____ **Explanation of Diagram:** - The diagram illustrates triangle \( \triangle ABC \) with a line \( BP \) forming two right triangles. - The right angle is at point \( P \), indicating that line \( BP \) is perpendicular to line \( AC \). - The triangles \( \triangle ABP \) and \( \triangle BPC \) are congruent by the given condition.
Transcribed Image Text:### Problem 32 **Given:** Triangle \( \triangle ABC \) is divided into two congruent triangles by line \( BP \). Fill in the blanks to show the congruent sides and angles. **Diagram:** The diagram shows triangle \( \triangle ABC \) with line \( BP \) dividing it into two smaller right triangles, \( \triangle ABP \) and \( \triangle BPC \). The right angle is marked at point \( P \). **Questions:** a. \( \overline{AP} \cong \) _____ b. \( \angle APB \cong \) _____ c. _____ \( \cong \angle PCB \) d. \( \triangle PBA \cong \) _____ **Explanation of Diagram:** - The diagram illustrates triangle \( \triangle ABC \) with a line \( BP \) forming two right triangles. - The right angle is at point \( P \), indicating that line \( BP \) is perpendicular to line \( AC \). - The triangles \( \triangle ABP \) and \( \triangle BPC \) are congruent by the given condition.
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