Similar and Congruent Figures Question
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In the questions below, choose the correct missing statements and reasons from the following proof.
Let line [math]l[/math] (not pictured) be parallel to side [math]bar{AC}[/math] in [math]Delta ABC[/math]. Line [math]l[/math] intersects [math]bar{AB}[/math] at point [math]D[/math] (not pictured) and [math]bar{BC}[/math] at point [math]E[/math] (not pictured). Prove that [math](AD)/(BD) = (CE)/(BE)[/math].
Let line [math]l[/math] (not pictured) be parallel to side [math]bar{AC}[/math] in [math]Delta ABC[/math]. Line [math]l[/math] intersects [math]bar{AB}[/math] at point [math]D[/math] (not pictured) and [math]bar{BC}[/math] at point [math]E[/math] (not pictured). Prove that [math](AD)/(BD) = (CE)/(BE)[/math].
| [math] \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \ [/math] | [math] \mathbf{"Reason"}[/math] |
| [math]1. l " || " bar{AC} [/math] | [math]1. ""[/math] |
| [math]2. ang BDE ~= ang A[/math] | [math]2. "If two || lines cut by a transversal, corr. angles congruent"[/math] |
| [math]3. ang B ~= ang B[/math] | [math]3. ""[/math] |
| [math]4. [/math] | [math]4. "AA Similarity Theorem"[/math] |
| [math]5. [/math] | [math]5. "Ratios corr. sides of similar triangles are equal"[/math] |
| [math]6. BD + AD = AB[/math] | [math]6. "Segment Addition Postulate"[/math] |
| [math]7. BE + CE = BC [/math] | [math]7. "Segment Addition Postulate"[/math] |
| [math]8. (BD + AD)/(BD) = (BE + CE)/(BE)[/math] | [math]8. "" [/math] |
| [math]9. (BD)/(BD) + (AD)/(BD) = (BE)/(BE) + (CE)/(BE) [/math] | [math]9. "Algebra (addition of fractions)"[/math] |
| [math]10. 1 + (AD)/(BD) = 1 + (CE)/(BE) [/math] | [math]10. "Any non-zero quantity divided by itself equals 1"[/math] |
| [math]11. (AD)/(BD) = (CE)/(BE) [/math] | [math]11. "Subtraction Property of Equality"[/math] |
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4
What is the missing reason in step 8?
- Ratios of corresponding sides of similar triangles are equal
- Division Property of Equality
- Substitution Property of Equality
- Corresponding sides of congruent triangles are congruent