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Common Core Standard HSG-CO.C.10 Questions

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

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Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 8?
  1. Corresponding angles of congruent triangles are congruent
  2. Corresponding angles of similar triangles are congruent
  3. AAA
  4. Definition of congruent angles
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 8?
  1. Sum of angles in a triangle is 180°
  2. Summation Property
  3. Definition of supplementary angles
  4. Substitution Property of Equality
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 1?
  1. Through any point and a line, there exists one perpendicular line
  2. Assume from diagram
  3. Given
  4. Two points define a line
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 5?
  1. Definition of isosceles triangle
  2. Given
  3. Assume from diagram
  4. Sides intersecting an altitude of a triangle are congruent
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 1?
  1. Two lines intersect in a point
  2. Parallel Postulate equivalent
  3. There exist an infinite number of lines in a plane
  4. Skew lines do not intersect
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing reason in step 3?
  1. Definition supplementary angles
  2. Definition perpendicular lines
  3. Definition vertical angles
  4. Angles on a straight line add up to 180°
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing statement in step 5?
  1. [math] ang EBC ~= ang BCA[/math]
  2. [math] ang ABC ~= ang BCA[/math]
  3. [math] ang EBA ~= ang ACB[/math]
  4. [math]ang DBC ~= ang CAB[/math]
Grade 10 Triangles CCSS: HSG-CO.C.10

This question is a part of a group with common instructions. View group »

What is the missing reason in step 3?
  1. Assume from diagram
  2. Given
  3. Definition of perpendicular lines
  4. Definition supplementary angles
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing statement in step 6?
  1. [math]bar{BD}~=bar{BD}[/math]
  2. [math]bar{AC}~=bar{AC}[/math]
  3. [math]bar{BC}~=bar{BC}[/math]
  4. [math]bar{AB}~=bar{AB}[/math]
Grade 10 Triangles CCSS: HSG-CO.C.10

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What is the missing statement in step 7?
  1. [math]triangle ABD ~= triangle BDC [/math]
  2. [math]triangle ABD ~= triangle DBC [/math]
  3. [math] triangle ABD ~= triangle CDB [/math]
  4. [math] triangle ABD ~= triangle CBD [/math]

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