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Geometry Warm-Up Quiz and Exercises

Test your geometry knowledge with questions about right triangles, slopes, midpoints, and distances. Practice using formulas to identify geometric shapes. Includes example problems with step-by-step explanations. Homework assignment: 9.7 worksheet.

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Geometry Warm-Up Quiz and Exercises

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  1. Warm Up Quiz • If the lengths of a right triangle are 5 and 10 what could the missing side be? [A] 75 [B] [C] 5 [D] 125 • If the hypotenuse of a 30-60-90 triangle is 30, what are the other two sides? • If the leg of a right-isosceles triangle is 9, what is the hypotenuse? • Find the distance between (-9,5) and (-7,3)

  2. Answers • B

  3. 9.7 Verifying Characteristics of a Geometric figure

  4. Formulas you need to know: • Slope formula • Slopes of parallel lines are ______________ • Slopes of perpendicular lines are _______________ • Midpoint formula • Distance formula equal Opposite reciprocals

  5. Ex1: Without graphing determine if a triangle is right, justify your answer. • Sides are A(-2,-1) B ( 1,2) C ( -2,5) • Think: A right triangle needs a right angle • Perpendicular lines form right angles • Which formula tells me something about perpendicular lines? • SLOPE – find the slope of each side (3) Slopes are opposite reciprocals, so the lines are perpendicular so we have a right angle so that means the triangle is right 

  6. Ex2: Classify the triangle by its sides defined by the points A(-3,5) B(-1,10) C(2,8) • We are working with sides, what formula will tell us the length of a side? • The distance formula. No sides are the same length therefore it is a scalene triangle.

  7. Justify the quad with sides A (3,1), B(1,5) C(9,9), D( 11,5)is a rectangle C B A D • Step 1: think what is the definition of a rectangle? • A parallelogram with 4 right angles and opposite sides are congruent • I need to find the slope of each side. DA and BC slopes are the same, and AB and CD slopes are the same so opposite sides are parallel so it is a parallelogram. The slopes of AB and AD are opposite reciprocals as are the slopes of BC and CD so the angles are right. Now check to see if the opposite sides are congruent.

  8. Justify the quad with sides A (3,1), B(1,5) C(9,9), D( 11,5)is a rectangle Use the distance formula to find the length of each side. AB and CD are the same length, and CB and AD are the same length. Since the angles are right angles, opposite sides are both parallel and congruent, this figure is a rectangle.

  9. Review/ summary: • Start with definition of shape you are trying to prove • Use the formulas • Answer the question in a complete sentence. Homework: 9.7 worksheet

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