Given: ; CE=CA ,EB AND AD are medians Prove: EB=AD 2.)Write a paragraph proof. Given: AC bisects <DAB and <DCB . Prove: DAC=BAC?
To prove that EB = AD given that CE = CA and EB and AD are medians, we can use the properties of medians in a triangle.
1. We know that in a triangle, a median divides the opposite side into two congruent segments.
2. Given that CE = CA, we can establish that the segments AE and AC are congruent.
3. Similarly, since EB is a median, it divides the side AD into two congruent segments, ED and DB.
4. Now we have two pairs of congruent segments, AE = AC and ED = DB.
5. By the transitive property of equality, we can conclude that AE = AC = ED = DB.
6. By the definition of a parallelogram, opposite sides of a parallelogram are congruent.
7. Since AD and EB are opposite sides of the parallelogram AECD, we can conclude that EB = AD.
Hence, we have proven that EB = AD.
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To prove that DAC = BAC, given that AC bisects angle DAB and angle DCB, we can use the properties of angle bisectors.
1. By definition, an angle bisector divides an angle into two congruent angles.
2. Given that AC bisects angle DAB, we can conclude that angle DAC is congruent to angle CAB.
3. Similarly, AC also bisects angle DCB, meaning angle BAC is congruent to angle CAD.
4. By the transitive property of equality, we can deduce that angle DAC is congruent to angle BAC.
Hence, we have proven that DAC = BAC.