Geometry Post-Assessment Study Notes

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Questions and Answers

Which two cities in Australia are farthest apart?

  • Sydney and Darwin
  • Darwin and Sydney
  • Perth and Sydney
  • Darwin and Perth (correct)

In triangle ABC, if m ∠ C < m ∠ B < m ∠ A, then AB < AC < BC is true.

True (A)

If Kyle has an angle of 45° and Jake has an angle of 65°, what is the measure of the third angle?

70°

In triangle dimensions, a set of lengths that can form a triangle must satisfy the ________.

<p>triangle inequality theorem</p> Signup and view all the answers

What could NOT be the dimensions of a triangular tile?

<p>3 mm, 9 mm, 14 mm (C)</p> Signup and view all the answers

What is the range of possible lengths for the third side of a triangle if the other two sides are 10 and 18?

<p>8 &lt; x &lt; 28</p> Signup and view all the answers

Which inequality represents the possible lengths for x in the figure with a side Ì…Ì…Ì…Ì… AB?

<p>3 &lt; x &lt; 14 (B)</p> Signup and view all the answers

Match the triangle properties with their definitions:

<p>Triangle Inequality Theorem = The sum of the lengths of any two sides must be greater than the length of the third side. Scalene Triangle = A triangle with all sides of different lengths. Isosceles Triangle = A triangle with at least two equal sides. Equilateral Triangle = A triangle with all sides and angles equal.</p> Signup and view all the answers

What is the range of lengths for the third side (s) of a triangle with sides measuring 4 inches and 7 inches?

<p>3 &lt; s &lt; 11 (A)</p> Signup and view all the answers

Which pair of measures could represent the lengths of the other two sides of a triangle if the longest side is 10 feet?

<p>4 ft., 7 ft. (C)</p> Signup and view all the answers

In triangle ABC, if side AB is the longest side, then m∠C could be greater than m∠A.

<p>False (B)</p> Signup and view all the answers

List the sides in order from greatest to least for triangle with sides measuring 7m, 10m, and 12m.

<p>12m, 10m, 7m</p> Signup and view all the answers

Which relationship correctly describes the angles of triangle ABC with sides 5 feet, 6 feet, and 7 feet?

<p>∠C &gt; ∠B &gt; ∠A (C)</p> Signup and view all the answers

A side length of 23 could be combined with two other sides to form a triangle. The two other sides must be less than ______.

<p>23</p> Signup and view all the answers

In triangle DEF, which angle represents the widest corner for placing the goat’s water?

<p>∠F (A)</p> Signup and view all the answers

What is the minimum length the third piece of spaghetti must be to form a triangle with lengths 5.2 cm and 2.4 cm?

<p>Greater than 2.8 cm and less than 7.6 cm</p> Signup and view all the answers

Given ∆APM, where AP = 37 and PM = 19, what are the possible lengths for AM?

<p>Between 18 and 56</p> Signup and view all the answers

Which of the following is the measure of angle D in triangle DEG?

<p>111° (D)</p> Signup and view all the answers

Which statement about triangle ABC is true given sides 7m, 10m, and 12m?

<p>m∠B &gt; m∠C (C)</p> Signup and view all the answers

Match the following sides with their order in triangle ABC where sides are 7m, 10m, and 12m:

<p>Longest side = 12m Second longest side = 10m Shortest side = 7m</p> Signup and view all the answers

In triangle ABC, if m ∠BAD = 130°, it is true that m ∠B < m ∠C.

<p>True (A)</p> Signup and view all the answers

If m ∠BAD = 130°, which option correctly describes relationship between angles C, B, and CAB?

<p>m ∠C = m ∠B and m ∠C &lt; m ∠CAB (D)</p> Signup and view all the answers

In triangle RST, if ∠R = 75°, then the sum of angles S and T must equal ________.

<p>105°</p> Signup and view all the answers

Match the following lengths of spaghetti with their possibility of being the third side in a triangle with sides 5.2 cm and 2.4 cm:

<p>2.4 cm = Not possible 2.8 cm = Possible 3.8 cm = Possible 7.7 cm = Not possible</p> Signup and view all the answers

Flashcards

Triangle Inequality Theorem

The sum of any two sides of a triangle must be greater than the third side.

Classifying Triangles by Sides

Triangles are classified by the lengths of their sides as equilateral, isosceles, or scalene.

Classifying Triangles by Angles

Triangles are classified by their angles as acute, right, or obtuse.

Triangle Inequality

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

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Possible Side Lengths of a Triangle

If two sides of a triangle have lengths a and b, the third side (c) must satisfy a + b > c, a + c > b, b + c > a.

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Triangle Sides

The lengths of the three sides of a triangle.

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Triangle Angle Relationships

The relationship between the angles and sides of a triangle. Larger side is opposite the larger angle.

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Triangle Angle Inequalities

If one angle in a triangle is bigger than another angle, the side opposite the bigger angle is longer.

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Triangle Side Length Range

The third side of a triangle must be greater than the absolute difference and less than the sum of the other two sides.

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Possible Triangle Sides

Given two side lengths, determine the possible values for the third side length to form a triangle

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Longest Side in Triangle

Given that one side of a triangle is the longest side, consider the possible lengths of the other two sides using the Triangle Side Inequality Theorem

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Triangle Angle Comparison

The side opposite a larger angle is greater than the sides opposite smaller angles.

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Triangle Side Ordering

Arrange the side lengths of a triangle from greatest to least based on their corresponding angles.

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Third Side Length (Triangle)

Find the range of possible values for the third side given the lengths of the other two.

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Possible Side Lengths for a Triangle

The lengths of three segments will form a triangle if the sum of any two sides is greater than the third.

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Triangle Side Inequality Theorem

In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

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Triangle Side Lengths and Angles

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. The relationship between side lengths and angles (side-angle relationships) is crucial in triangle geometry.

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Triangle Angle Sum (Theorem)

The sum of the interior angles in any triangle always equals 180 degrees.

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Triangle Inequality Theorem

The sum of any two side lengths of a triangle must be greater than the third side length.

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Finding Triangle Angles

To find the measure of a missing angle in a triangle, use the known angle measures and the triangle angle-sum theorem (the sum of the interior angles of a triangle equals 180 degrees).

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Largest Triangle Angle

The largest angle of a triangle lies opposite the longest side.

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Classifying Triangles by Angles

Triangles can be classified as acute (all angles less than 90 degrees), right (one angle is 90 degrees), or obtuse (one angle is greater than 90 degrees).

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Side Lengths to Angles

In a triangle, the longest side is opposite the largest angle, the shortest side is opposite the smallest angle

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Exterior Angle Theorem

An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

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Study Notes

Geometry Post-Assessment Study Notes

  • Problem 1: The question asks which two cities in Australia (Perth, Sydney, and Darwin) are furthest apart. The map depicts Darwin and Perth as the furthest apart.

  • Problem 2: Three boys (Kyle, Jake and another) are flying kites. The angles at Kyle and Jake are 45° and 65° respectively. The question asks for the distances between the boys in ascending order. KL, JK and LJ, in that order, are the correct answer. This is based on the provided angles and a triangle rule for relationships between sides and angles.

  • Problem 3: The provided information (In ∆ABC, if m∠C < m∠B < m∠A, then...) leads to the conclusion that the ordering of sides is BC < AB < CA.

  • Problem 4: Two triangles share a side. The question asks for the possible values of the shared side 'x'. The possible values for x are between 3 and 14.

  • Problem 5: A contractor is making new triangular-shaped tiles. The question is, which of the possible combinations/dimensions of triangle sides are invalid. Three mm, 9 mm, 14 mm are invalid.

  • Problem 6: Two sides of a triangle have lengths of 10 and 18. The question asks for the inequality that describes the possible lengths of the third side. That inequality is 8 < x < 28

  • Problem 7: The lengths of the sides of a triangle are given (AB = 5 feet, AC = 6 feet, and BC = 7 feet). The question asks for the relationship between the angles of the triangle. ∠A > ∠C > ∠B.

  • Problem 8: A farmer has three sections of fence to enclose a goat. The question asks which angle represents the widest corner. Answer: Angle D

  • Problem 9: Mrs. Lyons builds a triangle with spaghetti. The lengths of two pieces of spaghetti are given (5.2 cm and 2.4 cm). The question asks which of the provided lengths can be the third side of the triangle. Answer: 7.7 inches.

  • Problem 10: In triangle DEG, the question asks for the measure of angle D. The answer is 79°.

  • Problem 11: In ∆ABC (with point D), if ∠BAD is equal to 130°... The question asks for a true statement on the relative sizes of angles in the triangle. m∠C = m∠B, and m∠B < m∠CAB is TRUE.

  • Problem 12: In triangle RST, two angles are given. The question asks for the measures of the other two angles. ∠S = 55°, ∠T = 80°.

  • Problem 13: The question asks for the range of lengths of the third side of a triangle where the other two sides are 4 inches and 7 inches long. 3 < s < 11

  • Problem 14: A triangular garden has a longest side of 10 feet. The question asks for a pair of measures for the other two sides. The correct answer is 4 feet, 7 feet.

  • Problem 15: In a triangle (∆ABC), the question asks which statement about the angles is true. m∠B > m∠C is the answer.

  • Problem 16: Given the diagram of a triangle, the question asks to list the sides in order from greatest to least.

  • Problem 17: A side length of 23 is given. The question asks for two other sides, that when combined with 23, will form a triangle. The solution is 23 and 40

  • Problem 18: In triangle APM, where AP = 37, and PM=19. The question asks for possible lengths of AM. The list of possible lengths are: 36, 48, 56, 64.

  • Problem 19: In triangle CRM (where CR= 21cm, RM = 17cm, CM = 23cm), the question is listing in order the angles from least to greatest. ∠C, ∠R, ∠M is the correct order.

  • Problem 20: In triangle ABC, where angle A = 45° and angle C=110°. The question asks for the measure of angle B. The answer is 25°

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