Free Printable Triangle Inequalities

1.

Which side length could NOT form a triangle?

a)

5m, 6m, 8m

b)

10m, 10m, 2m

c)

19m, 34m, 15m

d)

3m, 16m, 14m

2.

Two sides of a triangle measure 10 feet and 14 feet. Which inequality shows the possible lengths for the third side, x?

a)

$10\le x\le14$

b)

$4\le x\le24$

c)

$10<x<14$

d)

$4<x<24$

3.

Two sides of a triangle measure 27 inches and 32 inches. Which could represent the length of the third side?

a)

5 in

b)

7 in

c)

59 in

d)

62 in

4.

Which inequality correctly shows the relationship of the angles in $\Delta JKL$ ?

a)

$m\angle K\ <\ m\angle L\ <\ m\angle J$

b)

$m\angle J\ <m\angle L\ <m\angle K$

c)

$m\angle L\ <\ m\angle J\ <\ m\angle K$

d)

$m\angle K\ <\ m\angle J\ <\ m\angle L$

5.

Which inequality correctly shows the relationship of the sides of $\Delta ABC$ ?

a)

$AC>BC>AB$

b)

$AC<BC<AB$

c)

$AB>BC>AC$

d)

$BC<AB<AC$

6.

Which inequality correctly shows the relationship of the sides shown in the diagram?

a)

$\overline{ZY}\ >\ \overline{WX}$

b)

$\overline{ZY}\ <\ \overline{XY}$

c)

$\overline{XY}\ =\overline{ZY}$

d)

$\overline{XY}<\overline{ZY}$

7.

In $\Delta PQR,$ $m\angle P=5x+7,$ $m\angle Q=3x-11,$ and $m\angle R=7x-26.$ Which inequality shows the relationship of the sides?

a)

$PR>PQ>QR$

b)

$PR<QR<PQ$

c)

$QR>PQ>PR$

d)

$PQ<QR<PR$

8.

In $\Delta CDE$ , $CD=2x+1$ , $DE=3x-4$ , and $CE=x+1$ . If the perimeter of the triangle is 52 meters, which inequality shows the relationship of the angles?

a)

$m\angle D<m\angle E<m\angle C$

b)

$m\angle D<m\angle C<m\angle E$

c)

$m\angle D>m\angle E>m\angle C$

d)

$m\angle D>m\angle C>m\angle E$

9.

In $\Delta MNP$ , $MN=5x+19$ , $NP=4x-1$ , and $MP=10x-7$ . Which inequality shows the possible values of x?

a)

$9<x<31$

b)

$3<x<25$

c)

$3<x<13$

d)

$11<x<25$

10.

In $\Delta RST$ , $RS=x+15$ , $ST=8x-26$ , and $RT=3x+1$ . Which inequality shows the possible values of x?

a)

$2<x<10.5$

b)

$2<x<4$

c)

$4<x<10.5$

d)

$4<x<26$

Triangle Inequalities

Total questions: 10

Worksheet time: 16mins

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