MATH SOLVE

4 months ago

Q:
# Please Help.Match the reasons to the statements given.

Accepted Solution

A:

Answer:1. Given2. Diagonals of a parallelogram bisect each other.3. Vertical angles are equal.4. Definition of parallelogram.5. If lines parallel, then alternate interior angles are equal.6. ASA7. CPCTEStep-by-step explanation:Statement 1:The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.Statement 2:BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence, [tex]BT = TD[/tex]Statement 3:Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.Statement 4:A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, [tex]BC ||AD[/tex] is because of the definition of a parallelogram.Statement 5:Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal. Statement 6:The triangles BET and DFT are now congruent because:i.Angle- [tex]\angle1=\angle2[/tex] ii. Side - [tex]BT = TD[/tex]iii. Angle - [tex]\angle3=\angle4[/tex]Therefore, by ASA postulate the two triangles are congruent.Statement 7:As the two triangles are congruent, then their corresponding parts are also equal.So, by CPCTE, [tex]ET=FT[/tex]