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1. Kayla wants to find the distance, AB, across a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 100 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.

a.Can Kayla conclude that  and  are congruent? Why or why not?

b. Suppose  ft. What can Kayla conclude? Explain.

 

 

2. Provide the missing reasons for the proof of part of the triangle midsegment theorem.

Given:   K is the midpoint of line segment MJ.

            L is the midpoint of line segment NJ .

Prove:    

Statement

Reason

1. K is the midpoint of line segment MJ. L is the midpoint of line segment NJ.

1.

2. Line segment MK is concngruent to line segment KJ and line segment NL is congurent to line segment LJ.

2.

3. MK = KJ and NL = LJ

3.

4. MJ = MK + KJ and NJ = NL + LJ

4.

5. MJ = 2KJ and NJ = 2LJ

5. Substitution Property of Equality

6. MJ/KJ = NJ/LJ = 2  

6. Division Property of Equality

7.

7.

8. JMN JKL

8.

9. MN/KL = MJ/KJ

9.

10. MN/KL = 2

10.

11. MN = 2KL

 

3. Complete the proof of the Pythagorean theorem.

Given: ABC is a right triangle, with
a right angle at

Prove: a^2 + b^2 = c^2

 

Given:  is a right triangle, with
a right angle at .

Prove:  

 

Answer:

Statement

Reason

1.  ABC is a right triangle, with a right angle
at

1. Given

2.   Draw an altitude from point C to line segment AB .

2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.

3.

3. Definition of altitude

4.

4. All right angles are congruent.

5.

5.

6.

6. AA Similarity Postulate

7. a/x = c/a

7.

8. a^2 = cx

8.

9.

9.

10.

adore.nuk  Jun 10, 2017
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1+0 Answers

 #1
avatar+75333 
+1

Here's the first one

 

Since angle ACB and  angle DCE are vertical angles, they are equal

And CB = CD

And angles CDE  and CBA are  right....so....

 

The two triangles are  congruent by Angle-Side-Angle

 

And since ED  = AB, then ED  will equal the distance across the river

 

 

 

 

cool cool cool

CPhill  Jun 12, 2017

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