A. Find at least three examples of congruent objects in a typical classroom. (don't need pictures).
What out of class activities could you employ to make students aware of congruent objects?

Stan is standing on the bank of a river wearing a baseball cap. Standing erect and looking directly at the other bank, he pulls the bill of his cap down until it just obscures his vision of the opposite bank. He then turns around, being careful not to disturb the cap, and picks out a spot that is just obscured by the bill of his cap. He then paces off the distance to this spot and claims that the distance across the river is approximately equal to the distance he paced. Is Stan's claim true? Why?

A building was to be built on a triangular piece of property. The architect was given the approximate measurements of the angles of the triangular lot as 54°, 39°, and 87° and the lengths of two of the sides as 100 m and 80 m. When the architect began the design on drafting paper, she drew a triangle to scale with the corresponding measures and found that the lot was considerably smaller than she had been led to believe. It appeared that the proposed building would not fit. The surveyor was called. He confirmed each of the measurements and could not see a problem with the size. Neither the architect nor surveyor could understand the reason for the other's opinion.

1.Explain why the architect felt she was correct.

2. Why did the surveyor feel he was correct?

3. Suggest a way to provide an accurate description of the lot.

The game of Triominoes has equilateral-triangular playing pieces with numbers at each vertex, shown as follows:

If two pieces are placed together as shown in the following figure, explain what type of quadrilateral is formed:

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If you asked your elementary students:

" What other games (board games or sporting games) have any geometric components?"

1. What might they respond?

2. What activities or projects might teachers initiate around their responses?

Please give a through explanation to the following. thank you
Answer true or false.
a. If each of two isosceles triangles has an angle that measures 120 degrees, then the two isosceles triangles must be similiar.
b. If each of two isosceles triangles has an angle that measures 40 degrees, then the two isosceles triangles m

In this question ABC and PQR are two triangles, and the lengths of the sides opposite the angles A,B,C P, Q, R are a,b,c,p,q,r, respectively.
Choose the THREE false statements.
Options.
A. If angle A= angle Q and angle B= angle P. then it must follow that c b
--- = --
r p
B. I

Please provide step-by-step solutions.
1 A drawing on a transparency is6.5 inches wide and 3 inches long. The width of the image of the drawing projected onto the screen is 13 feet. How long, in feet, is the drawing on the screen?
2. Triangles ABC and DEF are similar. The length of the sides of ABC are 56, 64, and 72

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above ground . When he is 10 feet from the base of the light,
(a) at what rate is the tip of his shadow moving?
(b) at what rate is the length of his shadow changing?
Answer: 25/3 feet per sec 10/3 feet per sec

Draw several kinds of triangles including a right triangle.
Draw a square on each of the sides of the triangles. Compute
the areas of the squares and use this information to investigate
whether the Pythagorean Theorem works for only
right triangles. Use a geometry utility if available.

1. Find two pythagorean triangles with the same area. Can you find any more with the same area?
2. Prove that two Pythagorean triangles with the same area and equal hypotenuses are congruent.

1- If we have a triangle ABC, then prove that the internal and external bisectors of the angle of a triangle are perpendicular (assume for angle A)
2- Prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles.

Please help me with the following problem:
a) Prove that two Pythagorean Triangles with the same area and equal hypotenuses are congruent.
b) Find two Pythagorean triangls with the same area.
Please show all work. Thanks in advance for the assistance.

1. For the two acute angles, m1=6x -3° and m2 =x + 2°. Solve for x and the measure of each angle. State the ideas from the tool kit that justify the procedure you use.
2. Find the minimum and maximum limits for the length of the third side of a triangle if the other two sides and 83' and 117'.