SOLUTION: Prove that a diagonal of a rhombus bisects each vertex angle through which it passes Given: ABCD is a rhombus, AC is a diagonal Statement: line AB in congruent to line BC Angl

Question 965887: Prove that a diagonal of a rhombus bisects each vertex angle through which it passes
Given: ABCD is a rhombus, AC is a diagonal
Statement: line AB in congruent to line BC
Angle 1 is congruent to angle 3
Line BC is II AC, AB is II to CD
<2 in congruent <3, <1 is congruent to <4
<1 is congruent to <2, <3 is congruent to <4
AC bisects I need help with the reasons for my statement, thank you
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Given: Rhombus ABCD with diagonal AC
To prove: ACF bisects ∠BAD and ∠BCD  



 1. AB ≅ CD            1. opposite sides of a parallelogram are congruent
 2. BC ≅ AD            2. opposite sides of a parallelogram are congruent
 3. AC ≅ AC            3. a line is congruent to itself.
 4. ΔABC ≅ ΔADC        4. SSS 1,2,3
 5. ∠1 ≅ ∠4            5. corresponding parts of congruent triangles.
 6. ∠3 ≅ ∠2            6. corresponding parts of congruent triangles.
 7. AB ≅ BC            7. definition of rhombus, all sides congruent.
 8. ΔABC is isosceles  8. two sides congruent, 7
 9. ∠1 ≅ ∠3            9. base angles of an isosceles triangle
10. ∠1 ≅ ∠2           10. things congruent to the same thing are equal 
                          to each other, 6,9 11. AC bisects ∠ABD   11. from 10
12. ∠3 ≅ ∠4           12. things congruent to the same thing are equal
                          to each other, 5,9
13. AC bisects ∠BCD   13. from 12 

Edwin

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