Exam 12: Congruence and Similarity With Constructions

Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties. -A triangle with angles of 31° and 85°

Answer the question. -John goes to a building and stands 100 feet away. He measures the angle of elevation to the top of the building as 37°. He also measures the angle of elevation 100 feet away from a different building. It is the same. He concludes that the buildings are the same height. Is he right? Explain.

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible". -

Provide the requested proof. - $\text { In the figure below, } \mathrm { BD } = \mathrm { CD } . \text { Prove that } \mathrm { m } ( \angle \mathrm { BAC } ) = 2 \mathrm {~m} ( \angle \mathrm { BAD } )$

Tell whether the triangles are similar or not similar. -

Answer the question. -Joe is building a deck. He nails a 10-foot, 2" by 8" board along the back of the house. He intends to use two 8-foot boards for the sides out to the corner posts. Then he will use another 10-foot board for the end. How can Joe make sure his deck is a rectangle, not a parallelogram, without checking the angles formed at the corners?

Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties. -A right triangle with legs (the sides including the right triangle)measuring a length of 33 cm and 6 cm

Tell whether the triangles are similar or not similar. -

What is needed to determine the congruency of two rhombuses?

Provide the requested proof. -In the figure below, $\mathrm { AB } = \mathrm { AE } , \mathrm { AC } = \mathrm { AD }$ and $\overline { \mathrm { AP } }$ is perpendicular to $\overline { \mathrm { BE } }$ . Prove that $\mathrm { BC } = \mathrm { DE }$ .

Provide the requested proof. - $\text { In the figure below, } \mathrm { BD } = \mathrm { CD } \text {. Prove that } \mathrm { m } ( \angle \mathrm { BAC } ) = 2 \mathrm {~m} ( \angle \mathrm { BAD } ) \text {. }$

Answer the question. -A lookout tower casts a shadow 150 feet long at the same time that the shadow of a 9 foot truck is 18 feet long. Find the height of the tower.

Answer the question. -When is a rectangle a parallelogram?

Solve. -Construct the perpendicular bisectors of the acute triangle.

Provide an appropriate response. -The two triangles shown below are congruent. The vertices corresponding to A, B, and C (in order) are .

Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties. -An isosceles triangle with two sides of length 4 cm and an apex angle of measure 74°

Solve. -Explain how to construct a square given one diagonal and constructing only perpendicular lines. If it is not possible, explain why.

Provide the requested proof. -Let $\angle I$ and $\angle \mathrm { E }$ be right angles, and suppose $\mathrm { ET } = \mathrm { IT }$ . Prove that the diagonals $\overline { \mathrm { KT } }$ and $\overline { \mathrm { EI } }$ are perpendicular.

Solve. -Construct the perpendicular bisectors of the obtuse triangle.

Solve. -Given an obtuse triangle ABC, explain how to construct an altitude from vertex A.