Provide the missing reasons for the proof given <C <E prove: ∆ABC ~DBE
2 answers:
For two triangles to be similar.
The ratio of their sides must be in proportion.(SSS)
Any two angles of one triangle must be equal to two angles of another triangle. (AA)
Ratio of two sides must be in proportion and the included angles must be congruent.
Here in the figure it is given that
<C = <E
Also
<ABC = <DBE as they are vertical angles.
So by AA
ΔABC ~ ΔDBE.
You might be interested in
Answer:
option D is true.
Step-by-step explanation:
The right-angled triangle is shown.
From the right-angled triangle,
The angle Ф = 60°
We know that the trigonometric ratio
tan Ф = opposite / adjacent
- opposite = 4
- adjacent = n
Thus,
tan 60 = 4 / n
√3 = 4/n
n = 4/√3
Thus,
n = 4/√3
= (4 × √3) / (√3 × √3)
= 4√3 / 3
Thus,
n = 4√3 / 3
Using Pythagorean theorem
m = √n²+4²
Thus,
- n = 4√3 / 3
Therefore, option D is true.