question 3: 20 pts
robyn wants to place a television set 8ft from her lounge chair. can the other two distances shown be 5ft and 9ft? identify the answer with the correct explanation.

Yes, the sum of any two lengths is greater than the third length

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

Applying the Triangle Inequality Theorem

1) 9+5 > 8 > is ok

2) 8+5 > 9 ---> is ok

3) 8+9 > 5 ---> is ok

therefore

Yes, the sum of any two lengths is greater than the third length

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.

10.4 inches

step-by-step explanation:

2x2x2.6