Question

which statements about the diagram are true? select three options. □ de + ef > df □ △ def is an isosceles triangle. □ 5 < df < 13 □ de + df < ef □ △ def is a scalene triangle.

Explanation:

Step1: Check triangle inequality for DE+EF>DF

Triangle inequality theorem: sum of two sides > third side. DE+EF>DF is always true for △DEF.

Step2: Verify isosceles triangle

Diagram shows DE=4, EF=9, DF≠4/9 (no equal sides). So not isosceles.

Step3: Check DF range

By triangle inequality: |EF-DE|<DF<EF+DE → |9-4|<DF<9+4 → 5<DF<13. True.

Step4: Check DE+DF<EF

DE=4, DF>5 → 4+5=9, so DE+DF>9=EF. False.

Step5: Verify scalene triangle

All sides DE=4, EF=9, DF (5-13, not equal to others) are distinct. True.

Answer:

DE+ EF > DF, 5<DF<13, △DEF is a scalene triangle