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Given: AC BD and CAB ZDBA. Prove: ABC ABAD. CAB LOBA

Given: AC BD and CAB ZDBA. Prove: ABC ABAD. CAB LOBA

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I have to prove that Triangle ABC is congruent to BAD.  i have to right the steps in order and give the reason.  I have no idea where to start.  Please help.

**Title: Geometry Proofs: Triangle Congruence** **Objective:** Given: - \( \overline{AC} \cong \overline{BD} \) - \( \angle CAB \cong \angle DBA \) Prove: - \( \triangle ABC \cong \triangle BAD \) **Instructions:** Use the equivalence properties to complete this proof. **Proof Table:** | Step | Statement | Reason | |------|-----------|--------| | 1 | \( AC \cong BD \) | Given | | 2 | \( \angle CAB \cong \angle DBA \) | Given | **Diagram Explanation:** The diagram displays two triangles, \( \triangle ABC \) and \( \triangle BAD \), intersecting at points \( C \) and \( D \), forming an 'X' shape. Lines \( \overline{AC} \) and \( \overline{BD} \) intersect, with point \( E \) as the intersection on the diagram. The congruent segments \( \overline{AC} \) and \( \overline{BD} \) are marked, along with congruent angles \( \angle CAB \) and \( \angle DBA \). **Note:** Lines \( \overline{AC} \) and \( \overline{BD} \) are segments. **Conclusion:** The goal is to prove \( \triangle ABC \cong \triangle BAD \) using the provided statements and reasons, assuming relationships given regarding segments and angles. Complete the proof using appropriate geometrical postulates.
Transcribed Image Text:**Title: Geometry Proofs: Triangle Congruence** **Objective:** Given: - \( \overline{AC} \cong \overline{BD} \) - \( \angle CAB \cong \angle DBA \) Prove: - \( \triangle ABC \cong \triangle BAD \) **Instructions:** Use the equivalence properties to complete this proof. **Proof Table:** | Step | Statement | Reason | |------|-----------|--------| | 1 | \( AC \cong BD \) | Given | | 2 | \( \angle CAB \cong \angle DBA \) | Given | **Diagram Explanation:** The diagram displays two triangles, \( \triangle ABC \) and \( \triangle BAD \), intersecting at points \( C \) and \( D \), forming an 'X' shape. Lines \( \overline{AC} \) and \( \overline{BD} \) intersect, with point \( E \) as the intersection on the diagram. The congruent segments \( \overline{AC} \) and \( \overline{BD} \) are marked, along with congruent angles \( \angle CAB \) and \( \angle DBA \). **Note:** Lines \( \overline{AC} \) and \( \overline{BD} \) are segments. **Conclusion:** The goal is to prove \( \triangle ABC \cong \triangle BAD \) using the provided statements and reasons, assuming relationships given regarding segments and angles. Complete the proof using appropriate geometrical postulates.
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