How many congruent triangles do the midsegments of an equilateral triangle partition the triangle into? explain.

4

Step-by-step explanation:

Let us consider an equilateral triangle ABC. Now, we will define midsegments:

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle (here triangle ABC). This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

Refer the attached image:

Now, from the definition of midsegment we can see that:

and PQ is also parallel to BR.

Now, again from the definition of midsegment we can see that:

and QR is parallel to PB.

therefore, PQBR forms a parallelogram

And a diagonal of a parallelogram divides it into two congruent triangles.

Hence, triangle 2 (triangle PBR) is congruent to triangle 4(triangle PQR).

Similarly, triangle 3 (triangle QRC) and triangle 1 (triangle APQ) are congruent to triangle 4 (triangle PQR), Therefore, there are 4 congruent triangles formed when midsegments of an equilateral triangle partition the triangle.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.