The two triangles shown are congruent: ΔABC ≅ ΔLMN.Based on this information, which of the following is a true statement?
1 answer:
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Answer:
A two column proof is presented as follows;
Statement Reason
1. AB ║ DE, BD bisects AE Given
2. ∠BAE = ∠AED, ∠ABD = ∠BDA Alternate ∠s are equal
3. =
,
=
By definition of bisection of line AE by BD
4. ΔABC ≅ ΔEDC By SAA, rule of congruency
Step-by-step explanation:
Step 1. AB ║ DE, BD bisects AE Given
Step 2. ∠BAE , ∠AED, and ∠ABD, ∠BDA are pairs of alternate angles formed by the parallel lines, AB and DE and are therefore, equal
Step 3. =
,
=
The bisection of line gives two lines of equal length. The bisection of AE by BD gives,
and
where
=
Similarly, the bisection of BD by AE gives, and
, where
=
Step 4. ΔABC ≅ ΔEDC By the Side-Angle-Angle (SAA), rule of congruency, which states that two triangles having two angles and the corresponding non included sides of each triangle equal to the other, the two triangles are congruent.