2) Determine if the following side lengths would create a triangle:
a) \(5, 7, 9\)
b) \(5, 12, 13\)
c) \(3, 10, 7\)
d) \(7, 12, 20\)
e) \(7, 7, 7\)
f) \(8, 2, 10\)
g) \( 6, 11, 4\)
h) \(24, 33, 11\)
i) \(12.3, 5.1, 17.2\)
j) \(\Large\frac{4}{7}, \frac{3}{7}, \frac{6}{7}\)
3) Give the two segments \(\overline{CA}\) and \(\overline{CB}\) connected by a hinge at point \(C\):
a) What is the maximum distance that can be made between points \(A\) and \(B\)?
b) What is the minimum distance that can be made between points \(A\) and \(B\)?
c) For \(\triangle ABC\) to be a triangle, what are the restrictions on the length of \(\overline{AB}\)?
a) \(5, 7, 9\)
b) \(5, 12, 13\)
c) \(3, 10, 7\)
d) \(7, 12, 20\)
e) \(7, 7, 7\)
f) \(8, 2, 10\)
g) \( 6, 11, 4\)
h) \(24, 33, 11\)
i) \(12.3, 5.1, 17.2\)
j) \(\Large\frac{4}{7}, \frac{3}{7}, \frac{6}{7}\)
3) Give the two segments \(\overline{CA}\) and \(\overline{CB}\) connected by a hinge at point \(C\):
a) What is the maximum distance that can be made between points \(A\) and \(B\)?
b) What is the minimum distance that can be made between points \(A\) and \(B\)?
c) For \(\triangle ABC\) to be a triangle, what are the restrictions on the length of \(\overline{AB}\)?
4) Given two sides of a triangle, what are the restrictions for the third side?
a) \(3, 5, x\)
b) \(8, 10, x\)
c) \(2.1, 3.4, x\)
d) \(5, 5, x\)
e) \(\Large\frac{4}{9}, \frac{7}{9}, \normalsize x\)
f) \(2, x, 3x\)
5) List the sides in order from shortest to longest for each triangle.
a) Given \(\triangle TOM\) with \(m\angle T = 50^{\circ}\), and \(m\angle O = 55^{\circ}\)
b) Given \(\triangle POR\) with \(m\angle P = 90^{\circ}\), and \(m\angle O = 42^{\circ}\)
c) Given \(\triangle TER\) with \(m\angle T = 65^{\circ}\), and \(m\angle E = 50^{\circ}\)
6) List the angles in order from smallest to largest:
a) Given \(\triangle NOW\) with \(NO = 8\), \(OW = 9\), \(NW = 10\)
b) Given \(\triangle YOU\) with \(YO = 4\sqrt 3\), \(OU = 4\), \(YU = 8\)
c) Given \(\triangle CAN\) with \(CA = 5\), \(AN = 3\), \(CN = 4\)
d) Given \(\triangle FLY\) with \(FL = 3\sqrt 2\), \(LY = 6\), \(FY = 3\sqrt 2\)
7) Do the three given side lengths form a triangle? If yes, give the order of the angles from smallest to largest. If no, then
state why not.
a) Given \(\triangle SHE\) with \(SH = 10\), \(HE = 6\), and \(SE = 8\)
b) Given \(\triangle SAW\) with \(AW = 8\), \(SA = 3\), and \(SW = 4\)
c) Given \(\triangle THE\) with \(TE = 15\), \(HE =\sqrt{675}\), and \(TH = 30\)
d) Given \(\triangle SUN\) with \(SU = \Large\frac{11}{14}\), \(UN = \Large\frac{4}{7}\), and \(SN = \Large\frac{2}{14}\)
8) Explain why the hypotenuse is always the longest side of a right triangle.
9) In an isosceles triangle, the base angles are always congruent. Explain why this is true using the concepts in this target.
a) \(3, 5, x\)
b) \(8, 10, x\)
c) \(2.1, 3.4, x\)
d) \(5, 5, x\)
e) \(\Large\frac{4}{9}, \frac{7}{9}, \normalsize x\)
f) \(2, x, 3x\)
5) List the sides in order from shortest to longest for each triangle.
a) Given \(\triangle TOM\) with \(m\angle T = 50^{\circ}\), and \(m\angle O = 55^{\circ}\)
b) Given \(\triangle POR\) with \(m\angle P = 90^{\circ}\), and \(m\angle O = 42^{\circ}\)
c) Given \(\triangle TER\) with \(m\angle T = 65^{\circ}\), and \(m\angle E = 50^{\circ}\)
6) List the angles in order from smallest to largest:
a) Given \(\triangle NOW\) with \(NO = 8\), \(OW = 9\), \(NW = 10\)
b) Given \(\triangle YOU\) with \(YO = 4\sqrt 3\), \(OU = 4\), \(YU = 8\)
c) Given \(\triangle CAN\) with \(CA = 5\), \(AN = 3\), \(CN = 4\)
d) Given \(\triangle FLY\) with \(FL = 3\sqrt 2\), \(LY = 6\), \(FY = 3\sqrt 2\)
7) Do the three given side lengths form a triangle? If yes, give the order of the angles from smallest to largest. If no, then
state why not.
a) Given \(\triangle SHE\) with \(SH = 10\), \(HE = 6\), and \(SE = 8\)
b) Given \(\triangle SAW\) with \(AW = 8\), \(SA = 3\), and \(SW = 4\)
c) Given \(\triangle THE\) with \(TE = 15\), \(HE =\sqrt{675}\), and \(TH = 30\)
d) Given \(\triangle SUN\) with \(SU = \Large\frac{11}{14}\), \(UN = \Large\frac{4}{7}\), and \(SN = \Large\frac{2}{14}\)
8) Explain why the hypotenuse is always the longest side of a right triangle.
9) In an isosceles triangle, the base angles are always congruent. Explain why this is true using the concepts in this target.