The Common Core Geometry curriculum focuses on teaching students about triangles and their properties. In Unit 1 Lesson 5, students learn about the Triangle Sum Theorem and the Exterior Angle Theorem. They are then given homework to practice these concepts, which includes a set of problems. This article will provide a summary of the Unit 1 Lesson 5 homework and the answers to each problem.
Overview of Common Core Geometry Unit 1 Lesson 5 Homework
The Unit 1 Lesson 5 homework focuses on three main topics: the Triangle Sum Theorem, the Exterior Angle Theorem, and solving equations involving triangles. The problems are designed to reinforce the concepts covered in class and help students develop their problem-solving skills.
The homework consists of a variety of question types, including multiple-choice, fill in the blanks, and short answer questions. Students need to apply their knowledge of triangle properties to determine missing angles, solve for x in equations, and justify their answers using the theorems learned in the lesson.
Detailed Answers to Common Core Geometry Unit 1 Lesson 5 Homework
The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. To find the value of angle A, we can subtract the given angles B and C from 180: A = 180 – B – C.
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. To find the value of angle D, we can add the measures of angles A and B: D = A + B.
To solve for x in the equation 2x + 3 = 7, we can subtract 3 from both sides: 2x = 4. Then, dividing both sides by 2, we get x = 2.
In a triangle, the sum of the measures of the three angles is 180 degrees. Given that one angle measures 60 degrees and another angle measures 90 degrees, we can find the measure of the third angle by subtracting the sum of the two known angles from 180: Third angle = 180 – 60 – 90.
By following these steps and applying the theorems and equations learned in Unit 1 Lesson 5, students can successfully complete the homework and reinforce their understanding of geometric concepts.
The Common Core Geometry curriculum’s Unit 1 Lesson 5 homework helps students practice triangle properties, the Triangle Sum Theorem, and the Exterior Angle Theorem. By solving problems to find missing angles and solve triangle equations, students understand these concepts better. Detailed answers in this article guide students through the homework.