Exam 12: Congruence and Similarity With Constructions

Solve. -Explain how to construct a parallelogram given two adjacent sides. If it is not possible, explain why.

Answer the question. -A quadrilateral is a______ if and only if opposite sides are parallel or congruent.

Provide the requested proof. - $\text { In the figure below, } \mathrm { AC } = \mathrm { AD } \text { and } \angle \mathrm { BAC } \cong \angle \mathrm { DAE } \text {. Prove that the triangle } \mathrm { ABE } \text { is isosceles. }$

If a rectangle is a square, it must also be a rhombus.

These triangles are similar. Find the missing length. -

Solve. -Describe how to draw a square so that a given circle circumscribes the square.

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 sides of length 19 cm, 9 cm, and 26 cm

Provide the requested proof. -Suppose polygon $\mathrm { ABCD }$ is any square with diagonals $\overline { \mathrm { AC } }$ and $\overline { \mathrm { BD } }$ intersecting at point $\mathrm { F }$ . What can be said about any point on $\overline { \mathrm { AF } }$ and points $\mathrm { B }$ and $\mathrm { D }$ ?

These triangles are similar. Find the missing length. -

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

Answer the question. -A tree casts a shadow 40 meters long. At the same time, the shadow cast by a vertical 5 meter stick is 10 meters long. Find the height of the tree.

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

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

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

Solve. -Given $\overline { \mathrm { AB } }$ , construct the perpendicular bisector of $\overline { \mathrm { AB } }$ without putting any marks below $\overline { \mathrm { AB } }$ .

Solve. -Explain how to construct a triangle with two obtuse angles. If it is not possible, explain why.

Answer the question. -What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

A sector of a circle is a pie-shaped section bounded by two radii and an arc. What is a minimal set of conditions for determining that two sectors of the same circle are congruent?

Answer the question. -Are two regular pentagons always similar? Explain why or why not.

Provide the requested proof. - $\text { In the figure below, } \mathrm { AB } = \mathrm { CD } , \mathrm { BE } = \mathrm { FC } \text { and } \angle \mathrm { B } \cong \angle \mathrm { C } \text {. Prove that } \mathrm { AF } = \mathrm { ED } \text {. }$