Given:
The given phrase is 16 seconds faster than Aya’s time.
To find:
The algebraic expression for the given phrase.
Solution:
Let x be the Aya’s time.
16 seconds faster than Aya’s time. It means 16 seconds less than Aya’s time.
We know that a negative sign "-" is used for less than.
16 seconds less than Aya’s time =
16 seconds faster than Aya’s time =
Therefore, the required algebraic expression is .
Answer:
The completed proof is presented as follows;
The two column proof is presented as follows;
Statements Reason
1. ║
, J is the midpoint of
1. Given
2. ∠IHJ ≅ ∠JLK 2. Alternate angles are congruent
3. ∠IJH ≅ ∠KJL 3. Vertically opposite angles
4. ≅
4. Definition of midpoint
5. ΔHIJ ≅ ΔLKJ 5. By ASA rule of congruency
Step-by-step explanation:
Alternate angles formed by the crossing of the two parallel lines and
, by the transversal
are equal
Vertically opposite angles formed by the crossing of two straight lines and
are always equal
A midpoint divides a line into two equal halves
Angle-Side-Angle, ASA rule of congruency states that two triangles ΔHIJ and ΔLKJ, that have two congruent angles, ∠IHJ in ΔHIJ ≅ ∠JLK in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent
≅
, then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.
