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TEKS: G2B, G8C The student will make conjectures about segments. The student will use tools to determine measurements of geometric figures This means that the angles do not overlap. Example: 1 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. AEB and BED Adjacent and Linear Pair AEB and BEC Adjacent Only DEC and AEB Not Adjacent Example: 2 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 5 and 6 Adjacent and Linear Pair 7 and SPU Not Adjacent 7 and 8 Not Adjacent Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical angles are two nonadjacent angles formed by two intersecting lines. 1 and 3 are vertical angles, as are 2 and 4. Example: 3 Name the pairs of vertical angles. HML and JMK are vertical angles. HMJ and LMK are vertical angles. Check mHML mJMK 60°. mHMJ mLMK 120°. Example: 4 Name a pair of vertical angles. Do they appear to have the same measure? Check by measuring with a protractor. EDG and FDH are vertical angles and appear to have the same measure. Check mEDG ≈ mFDH ≈ 45° Construct an angle congruent to ∡A. A Step 1: Use a straight edge to draw a ray with endpoint D. D B Construct an angle congruent to ∡A. Step 2: Place the compass point at A and draw an arc that intersects both sides of ∡ A. Label the intersections points B and C. D C A B Construct an angle congruent to ∡A. Step 3: Using the same compass setting, place the compass point at D and draw an arc that intersects the ray. Label the intersection E. C A D E B Construct an angle congruent to ∡A. Step 4: Place the compass point at B and open it to the distance BC. Tighten the compass to keep its distance. C A D E B Construct an angle congruent to ∡A. Step 5: Place the point of the compass at E, without changing its size, and draw an arc. Label its intersection with the first arc F. C F A D E B Construct an angle congruent to ∡A. C A F Step 6: Use a straight edge to draw DF D E Construct the bisector of ∡A. Step 1: Place the point of the compass at A and draw an arc. Label its points of intersection with ∡A as B and C. A B A C Construct the bisector of ∡A. Step 2: Without changing the compass setting, draw intersecting arcs from B and C. Label the intersection of the arcs as D. B D A C Construct the bisector of ∡A. Step 3: Use a straight edge to draw AD. AD bisects ∡A. B D A C