Given AD CB ADB CBD Prove: ∆ADB ≅ ∆CBD

Mathematics

2 answers:

algol [13]2 years ago

8 0

Answer:

<h2>SAS postulate.</h2>

Step-by-step explanation:

Notice that sides AD and BC are congruent, also DB is a common side to both triangles. At this point, we already have two corresponding congruent sides.

Additonally, angles ADB and CBD are congruent. In summary, we have two pair of corresponding sides congruent, and one pair of corresponding angles congruent (which is formed by the congruent sides).

Based on all the given information, by SAS postulate triangles ADB and CBD are congruent.

Andrei [34K]2 years ago

7 0

We will use the SAS (SIDE-ANGLE-SIDE) to prove that two triangles are congruent.

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If two triangles have equal perimeters, then they could also have which of the following? Select all that apply.

Radda [10]

Answer: The answers is (B) equal areas.

Step-by-step explanation: Given that two triangles have equal perimeters.

As shown in the attached figure, let us consider two right-angles triangles, ΔABC and ΔDEF, with sides AB = 3 cm, BC = 4 cm, AC = 5 cm, DE = 4 cm, EF = 3 cm and DF = 5 cm.

So the perimeters of both the triangles = 3 + 4 + 5 = 4 + 3 + 5 = 12 cm.

Since volume term is not valid in case of triangles, so they cannot have equal volumes. Therefore, option (A) is incorrect.

Area of ΔABC is

$A_{ABC}=\dfrac{1}{2}\times AB \times BC = \dfrac{1}{2}\times 3\times 4=6~\textup{cm}^2,$

and area of ΔDEF is

$A_{DEF}=\dfrac{1}{2}\times DE\times EF=\dfrac{1}{2}\times 4\times 3=6~\textup{cm}^2.$

Therefore, they may have equal areas and so option (B) is correct.

If the triangles have equal bases, then the heights will also be equal and both the triangles will be same. Similar is the case with equal heights. So, options (C) and (D) are incorrect.

Thus, the correct option is (B). equal areas.