Transformation & Congruence
Two shapes look the same but one is flipped upside down. What transformation was applied?
Reflection (or flip)
Two parallel lines are cut by a transversal. If one alternated interior angle measures 65 degrees, what is the measure of its alternate interior angle ?
65 degrees.
The three angles of a triangle sum to how many degrees ?
180 degrees
You want to construct a triangle with sides 3 cm, 4cm, and 8 cm. Why is this impossible ?
The sum of any two sides must be greater than the third side. Here 4 + 3 = 7, which is not greater than 8.
A regular hexagon has all sides equal and all angles equal. What is the measure of each interior angle. ( a hexagon has 6 sides)
120 degrees
Which Statement is NOT true about congruent figures ?
1. They have the same size and shape.
2. They can be created by rigid transformations.
3. They must have the same color.
4. One figure can be rotated to match the other.
3. They must have the same color.
If two parallel lines are cut by a transversal , what is the relationship between corresponding angles ?
Corresponding angles are congruent.
In triangle ABC, angle A measures 35 degrees, angle B measures 78 degrees. What is the measure of angle C?
67 degrees
What is the triangle inequality theorem ?
The sum of any two sides of a triangle must be greater than the length of the third side.
What is the name of a polygon with 8 sides ?
Octagon
Two triangles have the same three side lengths. Are they congruent? Explain your reasoning.
Yes, they are congruent.
(Identical side lengths, SSS Congruence)
110 degrees
Can a triangle have two right angles? Why or why not?
No, because two right angles already sum to 180 degrees, leaving no degrees for the third angle.
Yes because 5 +5 = 10, which is greater than 9. 9+5 =14, which is greater than 8.
A regular Pentagon has 5 equal angles. What is the sum of all interior angles in a pentagon ?
540 degrees. (5-2) X 180 degrees = 540 degrees
A transformation slides a shape 5 units right and 3 units down. What is the transformation called, does it create a congruent figure?
Translation (Slide). Yes it creates a congruent figure because translation are rigid transformations.
A line is parallel to one side of a triangle and intersects the other two. What geometric concept relates the angles formed ?
The angles formed are congruent to the original angles of the triangle or alternate interior angles are formed.
Which set of angle measures can form a triangle ?
45, 45, 91 or 60, 60, 60
60, 60, 60
What is the maximum length for the third side of a triangle if two sides are 6 cm and 4 cm?
The third side must be less than 10 cm
Find the measure of each interior angle of a regular pentagon.
108 degrees
(540 degrees divided by 5 equals 108 degrees)
If a figure is rotated 180 degrees around a point, then reflected across a line, is the result congruent to the original ? Why or why not?
Yes, it is congruent. Both rotation and reflection are Rigid transformations, and the composition of rigid transformations is also rigid.
If a transversal crosses two lines and creates a 75 degree angle on one line and the corresponding angle on the second line is also 75 degrees, what can you say about the two lines?
The two lines are parallel.
If one angle of a triangle is 90 degrees and another is 45 degrees, what is the measure of the third angle, and what special name does this triangle have?
The third angle is 45 degrees. This is a 45-45-90 triangle ( isosceles right triangle)
Two sides of a triangle are 7 cm and 3 cm. What is the range of possible lengths for the third side ?
The third side must be greater than 4 cm and less than 10 cm.
What is the formula for finding the sum of interior angles in any polygon ?
n-2 times 180 degrees, where n is the number of sides.