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Solve for X A

Solve for X A

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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Question
**Solve for X** The image presents two triangles, △BDC and △BAC. These triangles share the same vertex B and form a single larger triangle △BDC, with line segment AC acting as a base shared between the smaller triangles. The following details can be observed: - Triangle △BDC is the larger triangle with vertices labeled D, B, and C. - Triangle △BAC is inside △BDC, sharing side AC with the larger triangle. The point A lies on the base DC. **Marked Equal Lengths:** - Segments BA and BC have tick marks, indicating that these two are of equal length. - Segments DA and AC have tick marks, indicating these are of equal length. **Variables:** - The length of segment DA is marked as "X." - Segment AC is marked with the same tick as segment DA, indicating they have the same length. **Objective:** The goal is to solve for the variable \( X \). Since DA and AC are congruent, this indicates that within △BDC, DA = AC = \( X \). If additional numerical information or angles were given, proportions or congruent triangle properties could be applied further. The main geometrical rules hinted by this setup include congruent segments and the properties of isosceles triangles. Thus, understanding congruent parts can allow solving for unknowns like \( X \).
Transcribed Image Text:**Solve for X** The image presents two triangles, △BDC and △BAC. These triangles share the same vertex B and form a single larger triangle △BDC, with line segment AC acting as a base shared between the smaller triangles. The following details can be observed: - Triangle △BDC is the larger triangle with vertices labeled D, B, and C. - Triangle △BAC is inside △BDC, sharing side AC with the larger triangle. The point A lies on the base DC. **Marked Equal Lengths:** - Segments BA and BC have tick marks, indicating that these two are of equal length. - Segments DA and AC have tick marks, indicating these are of equal length. **Variables:** - The length of segment DA is marked as "X." - Segment AC is marked with the same tick as segment DA, indicating they have the same length. **Objective:** The goal is to solve for the variable \( X \). Since DA and AC are congruent, this indicates that within △BDC, DA = AC = \( X \). If additional numerical information or angles were given, proportions or congruent triangle properties could be applied further. The main geometrical rules hinted by this setup include congruent segments and the properties of isosceles triangles. Thus, understanding congruent parts can allow solving for unknowns like \( X \).
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