Question 32 • CMS 2026-2027 Foundations of Math 3 INITIAL CREDIT
Statements Reasons 1. line segment AB is parallel to over left right arrow DE 1. given 2. angle 1 and angle 3 are corresponding angle s; angle 2 and angle 4 are corresponding angle s 2. def. of corresponding angles 3. angle 1 is congruent to angle 3 ; angle 2 is congruent to angle 4 3. corresponding angle s thm. 4. triangle ABC approximates triangle DEC 4. AA similarity thm. 5. ? 5. definition of similar triangles 6. AC is equal to AD plus DC ; BC is equal to BE plus EC 6. segment addition postulate 7. the fraction with numerator AD plus DC and denominator DC is equal to the fraction with numerator BE plus EC and denominator EC 7. substitution 8. AD over DC plus DC over DC is equal to BE over EC plus EC over EC 8. addition of fractions 9. AD over DC plus 1 is equal to BE over EC plus 1 9. simplification of fractions 10. AD over DC is equal to BE over EC 10. subtraction property What is the missing statement in Step 5?
Answer
A
AC over DC is equal to BC over EC
B
AD is equal to BE
C
AC is equal to BC
D
AD over DC is equal to BE over EC
Explanation
Since triangle ABC is similar to triangle DEC, corresponding sides are proportional. The matching sides are AC with DC and BC with EC, so AC/DC = BC/EC. This is the definition of similar triangles, making choice A correct.
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