Answer :
(2) The statements and reasons in the two-column method are presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{BD}[/tex] bisects ∠ABC [tex]{}[/tex] 1. Given
2. ∠BAD ≅ ∠BCD [tex]{}[/tex] 2. Given
3. ∠ABD ≅ ∠CBD [tex]{}[/tex] 3. Definition of angle bisector
4. [tex]\overline{BD}[/tex] ≅ [tex]\overline{DB}[/tex] [tex]{}[/tex] 4. Reflexive property
5. ΔABD ≅ ΔCBD [tex]{}[/tex] 5. AAS congruency postulate
(3) The two-column method used to prove the congruency of triangles ΔQRS and ΔSTU, is presented as follows;
Statement [tex]{}[/tex] Reason
1. S is the midpoint of [tex]\overline{QU}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex] [tex]{}[/tex] 2. Given
3. [tex]\overline{RS}[/tex] ≅ [tex]\overline{TU}[/tex] [tex]{}[/tex] 3. Given
4. [tex]\overline{QS}[/tex] ≅ [tex]\overline{SU}[/tex] [tex]{}[/tex] 4. Definition of midpoint of [tex]\overline{QU}[/tex]
5. ΔQRS ≅ ΔSTV [tex]{}[/tex] 5. SSS congruency postulate
What is the two-column method used to prove geometric statements?
The two column method consists of statements and the associated reasons arranged sequentially side by side in a two-column tabula format.
The reasons used to prove the above statements are as follows;
Angle bisector
An angle bisector is a segment that divides an angle into two angles of the same measure.
Reflexive property
The reflexive property of equality states that the value of an object or the measure of a dimension is equal to itself
AAS congruency postulate
AAS which is the acronym for Angle-Angle-Side congruency, states that if two angles and a non included side of one triangle are congruent to two angles and the non included side of another triangle, then the two triangles are congruent
Midpoint of a line
The midpoint of a line is a point that divides the line into two segments of the same measure.
SSS congruency postulate
The Side-Side-Side congruency postulate states that two triangles are congruent if three sides are congruent to three sides of the other triangle
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