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Math Warm-Up Activities for Angle Relationships

This collection of math warm-up activities focuses on angle relationships, including linear pairs and vertical angles. Students will explore the properties of these angles and solve for missing measures using algebraic equations.

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Math Warm-Up Activities for Angle Relationships

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  1. Year 2 Warm Up 1. -6; -28,-34,-40 2. 4; 12,16,20 For #1-2 find the rule, then find the next three terms in the sequence. 1. 2 ,-4,-10, -16, -22… 2. -8, -4, 0, 4, 8… 3. Find the slope of (-8, 7) and (-8, 6) 4. Find the slope of (-2, 7) and (-8, 7) 3. undefined 4. m=0

  2. 2.5 Angle Relationships • Investigation 1 “The Linear Pair Conjecture” • Step 1) Draw PQ with point R between points P and Q. • Step 2) Draw RS – Now you have a Linear Pair • Step 3) Label the angles <1 and <2. • Step 4) Use your protractor to measure <1 and <2. • Step 5) Compare your results for your two angles’ measures with your group or a classmate. • What do you notice about the two angles? Linear Pair Conjecture

  3. Angle Relationships • Linear Pair Conjecture – If two angles form a linear pair, then the measures of the angles add up to 180 degrees. 1 2 <1+<2=180 °

  4. 1 4 2 3 Angle Relationships • Investigation 2 “Vertical Angles Conjecture” • Step 1) Draw two intersecting lines that are not perpendicular onto patty paper. Label the angles as shown: • Which angles are vertical? • Step 2) Fold the patty paper so that one pair of vertical angles lie over each other. Vertical Angles Conjecture

  5. 1 4 2 3 • What do you notice about their measure? • Vertical Angles Conjecture: If two angles are vertical angles, then they are congruent. <1=<3 <2=<4

  6. a b c 130° Find the missing measures • Ex 1) a = b = c = 50° 130° 50°

  7. a c b 65° Find the missing measures • Ex 2) a = b = c = 90° 25° 90°

  8. Find the missing measures • Ex 3) a = b = c = d = 30° 100° 50° 100° b a c 30° 50° d

  9. m<1 = 3x-40 2x-10 = m<2 Algebra with Angles – Ex 1 • State the type of angles • State the relationship • Solve for x. • Then find measure of each angle.

  10. Answer 1 The angles are vertical, therefore they are congruent. This means that the measures of each angle are equal. m<1 = m<2 3x-40 = 2x – 10 x – 40 = -10 x = 30 Step 1: Set up the angle relationship. Step 2: Substitute in values. Step 3: Solve for x. Step 4: Plug back in to find angle measures. m<1 = 3(30) - 40 m<2 = 2(30) - 10 m<1 = 50° m<2 = 50°

  11. m<2 =x m<1 = 4x - 20 Algebra with Angles – Ex 2 • State the type of angles • State the relationship • Solve for x • Find the measure of angle 1.

  12. Answer – Ex. 2 <1 and <2 form a line making them a linear pair which adds up to 180 degrees. Therefore, m<1 +<2 = 180° (4x – 20) + (x) = 180 5x – 20 = 180 5x = 200 x = 40° m<2 = 40°, m<1 = 140° Step 1: Set up the angle relationship. Step 2: Substitute in values. Step 3: Solve for x. Step 4: Plug back in to find angle measures.

  13. Summary : Make a chart below showing the angle types(vertical, linear pair, and right angles), their relationships(congruent, supplementary, complementary), and a sketch for each.

  14. Homework In Class Practice Classwork 2.5 Worksheet and Bookwork p. 122 #1-6…you must copy the pictures and show your work!!! • Homework 2.5 worksheet

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