Geometry- Triangles and Their Side Lengths assignment

Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle exists because the sum of any two side lengths is greater than the length of the third side. This triangle exists because the sum of 4 and 12 is less than 17. This triangle does not exist because the sum of any two side lengths is greater than the length of the third side. This triangle does not exist because the sum of 4 and 12 is less than 17.

d. This triangle does not exist because the sum of 4 and 12 is less than 17.

In triangle ABC, AB measures 25 cm and AC measures 35 cm. The inequality < s < represents the possible third side length of the triangle, s, in centimeters. The inequality < p < represents the possible values for the perimeter, p, of the triangle, in centimeters.

10 60 70 120

Under which angle conditions could a triangle exist? Check all that apply. 3 acute angles 2 acute angles, 1 right angle 1 acute angle, 1 right angle, 1 obtuse angle 1 acute angle, 2 obtuse angles 2 acute angles, 1 obtuse angle

3 acute angles 2 acute angles, 1 right angle 2 acute angles, 1 obtuse angle

A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n? 5 < n < 15 5 < n < 20 15 < n < 20 15 < n < 25

d. 15 < n < 25

Mr. Anderson is building a triangular-shaped roof for his shed. The triangle must be isosceles with its base (noncongruent) side measuring 14 feet. The length of one of the congruent legs must be greater than what value? x > feet

7

Triangle DEF contains two congruent acute angles. The sum of the measures of the two congruent acute angles is greater than 90 degrees. Anna concludes that the triangle must be an acute triangle. Which best describes her conclusion? She is correct. A triangle having at least one acute angle is an acute triangle. She is correct. The remaining angle of the triangle measures less than 90 degrees. She is incorrect. The angles measure greater than 90 degrees so the triangle is obtuse. She is incorrect. The third angle in a triangle with two congruent acute angles is a right angle.

b. She is correct. The remaining angle of the triangle measures less than 90 degrees.

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C? How far would Pete walk if he went from A to B to C? yards The direct distance from A to C is more than yards. The inequality w < represents the distance, w, that Pete might save by taking the direct path.

40 10 30

Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.

Triangles has the following rule: a + b > c where c is the length of the bigger side and a and b is the length of the other sides. If you form a triangle from two congruent wooden dowels, then you will have that the sum of the length of the two lesser sider is equal to the longer sides, violating the rule established before. Therefore, a triangle cannot be formed with the 3 pieces.

Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles? 2 in., 4 in., 6 in. and 3 in., 5 in., 7 in. 2 in., 5 in., 6 in. and 3 in., 4 in., 7 in. 2 in., 3 in., 4 in. and 5 in., 6 in., 7 in. 2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.

c. 2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply. m∠R > 90° m∠S + m∠T < 90° m∠S = m∠T m∠R > m∠T m∠R > m∠S m∠S > m∠T

m∠R > 90° m∠S + m∠T < 90° m∠R > m∠T m∠R > m∠S