Prove \triangle ABE\cong\triangle ACE△ABE≅△ACE. Be sure to state any congruencies and the criteria used to determine them.

The answer is below

Step-by-step explanation:

Two triangles are congruent if they have the same shape and their corresponding sides are equal to each other.

1) AB = DC, BE = CE     (given)

2) ∠AEB≅∠DEC  (vertical angles are congruent)

3) ΔABE ≅ ΔACE (side angle side congruence theorem)

If the two sides and an included angle of one triangle is equal to two sides and one included angle of another triangle, then the two triangles are congruent by SAS congruence theorem.

Given : graph  describing the journey of a bus between two stops.

To find : acceleration  in the first 20 s ,  the distance between two stops ,  k average speed of the bus

Solution:

From Graph

Time sec     Velocity  m/s

0                   0

20                 7

130                7

160                0

acceleration, in m/s in the first 20 s

= ( 7 - 0 ) / (20  - 0)

= 7/20

= 0.35  m/s²

Distance between two stops

= (1/2) (0 + 7) * (20 -0)    + 7 * ( 130 - 20)  +  (1/2)(7 + 0)(160-130)

= 70  + 770 + 105

= 945 m

Average Speed =  945/160   =  5.9  m/s