Which statements about the diagram are true? select three
options.
de + ef > df
a def is an isosceles triangle.
5 o
a def is a scalene triangle.

Answer : The correct options are:

DE + EF > DF

5 < DF < 13

Δ DEF is a scalene triangle.

Step-by-step explanation :

As we know that there are three types of triangle.

(1) Equilateral triangle : It is a triangle in which the three sides and angle are equal.

(2) Isosceles triangle : It is a triangle in which the two sides and two angle are equal.

(3) Scalene triangle : It is a triangle in which the three sides and angle are not equal.

Now we have to determine the length DF.

using Pythagoras theorem:

The length DF = 8.06 unit

So, we can say that:

DE + EF > DF

Hence, from the given options we conclude that, the correct options are:

DE + EF > DF

5 < DF < 13

Δ DEF is a scalene triangle.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.