Congruence, Quadrilaterals, Similarity & Dilation, Pythagorean Theorem and Converse
Name: ______Date: ______Pd: _____
Review - Geometry Benchmark 2
Congruence, Quadrilaterals, Similarity & Dilation, Pythagorean Theorem and Converse,
Special Right Triangles, Right Triangle Trigonometry
Congruence
What must be true for two polygons to be congruent to each other?
List the 5 postulates or theorems that allow us to prove two triangles are congruent.
What does “cpctc” stand for?
Quadrilaterals
List 6 ways we can prove a quadrilateral is a parallelogram.
A rhombus has all the properties of a parallelogram. What additional special properties does it have?
A rectangle has all the properties of a parallelogram. What additional special properties does it have?
A square has all the properties of a parallelogram. What additional special properties does it have?
What are the properties of a trapezoid? Of an isosceles trapezoid?
How do you find the midsegment of a trapezoid?
What are the properties of a kite?
Similarity and Dilations
List the 3 postulates or theorems that allow us to prove two triangles are similar.
How does the geometric mean relate to similarity?
Give an example of the Side-Splitter Theorem.
Give an example of the Triangle Angle Bisector Theorem.
Describe how you would dilate a figure on the coordinate plane if the center of dilation is the origin.
Describe how you would dilate a figure on the coordinate plane if the center of dilation is a point other than the origin.
Describe how you would find the center of dilation given a pre-image and an image.
Pythagorean Theorem and Converse
What is the Pythagorean Theorem?
How can we classify triangles as acute, right or obtuse?
What are some common Pythagorean triples?
Special Right Triangles
What is the ratio of sides in a 45-45-90 triangle?
What is the ratio of sides in a 30-60-90 triangle?
Right Triangle Trigonometry
Describe the ratio of sides for the sine, cosine, and tangent of an acute angle in a right triangle.
If the triangles are congruent, state the postulate or theorem that allows you to prove it.
- The figure shows with side lengths as indicated. Find the value of x.
A triangle with side lengths 5, 11, and 15 is similar to another triangle with longest side length of 24.
A) What is the scale factor of the first triangle to the second triangle?
B) What is the perimeter of the larger triangle?
- A triangular park is formed by the intersections of three streets, Bridge Street, Harbor Place, and College Avenue, as shown in the diagram. A 21-yard walkway parallel to Harbor Place goes through the park. The stretch of College Avenue between Harbor Place and the walkway is 12 yards. What is the perimeter of the entire park?
14.
15.
16.
17.
18.
19.
20.
Find the value of x.
21.
22.
23.
An unmanned aerial vehicle (UAV) is equipped with cameras used to monitor forest fires. The figure represents a moment in time at which a UAV, at point B, flying at an altitude of 1,000 meters is directly above point D on the forest floor. Point A represents the location of a small fire on the forest floor. At the moment in time represented by the figure, the angle of depression from the UAV to the fire has a measure of 300. (6 pts)
A) At the moment in time represented by the figure, what is the distance (to the nearest meter) from the UAV to the fire?
B) What is the distance (to the nearest meter) from the fire to point D?
24.
25.