Triangles
△ABC is a right triangle. If AB = 4 and BC = 3, what is the length of AC?
How do you find the length of the hypotenuse of a right triangle?
If dilation is not a rigid motion, then it does not preserve anything. True or false?
What do you know about the side lengths and angle measures of similar triangles?
What are some important theorems you have learned regarding congruent triangles?
Which theorem is invalid for proving that triangles are congruent?
There are only three trigonometric functions. True or false?
How many trigonometric functions can you name?
How many sides does a heptagon and a decagon have?
How many years are there in a decade?
What is the difference between a supplementary angle and a complementary angle?
If two angles add up to 90 degrees, what are they called?
If I would like to describe a dilation , i would like to know the center of dilation and the scale factor, so what is needed for a reflection ?
Two triangles have the following measurements:
Triangle A: sides of lengths 5, 7, and 9
Triangle B: sides of lengths 5, 7, and 9
When solving a problem using trigonometry, should you begin with an angle or a side? Explain why.
If you begin with an angle, what steps can you take next? How does the approach change if you begin with a side?
What is the minimum number of degrees you can rotate a heptagon so that it maps onto itself?
If any shape maps onto itself after a 360° rotation, how is a 360° rotation helpful?
In triangle ABC:
AB=6
BC=9
AC=12
a) Which angle of triangle ABC has the greatest measure?
If the shortest side of a triangle is opposite the smallest angle, which side is opposite the largest angle?
When dilating a line and the center of dilation is not on the line, what can you say about the image of the dilation?
Triangles RST and XYZhave the following information:
∠R≅∠X
∠S≅∠Y
RS≅XY
Are triangles RST and XYZ congruent?
Which congruence theorem can be used in this situation?
A surveyor stands 40 feet from the base of a flagpole on level ground. The angle formed between the ground and the line of sight from the surveyor’s eye to the top of the flagpole measures 28°.
Determine the height of the flagpole, to the nearest tenth of a foot.
How would you draw a diagram to represent this situation?
When a transversal intersects parallel lines, which angles are congruent to each other?
If two sides of a triangle have the same length, we call it an isosceles triangle. If none of the sides are the same length, what do we call it?
Is the triangle equilateral?
If you rotate a point 180 degrees, what other transformation would result in the same image?
Which transformation can be ruled out immediately?
Triangles △PQR and △PTS are congruent.
The measure of ∠Q =3x+12
The measure of ∠T= 5x - 8
Find the value of x
What is the relationship between the two given angles?
In right triangle ABC, angle C is a right angle.
SinA = (3x+5) and the measure of CosB = 5x−25 ,what is the value of x ?
What do you know about the trig cofunction properties?
Points A(2,−4) and B(8,6) are endpoints of a directed line segment AB
Point P divides AB in the ratio 2 : 3, such that
AP:PB=2:3 2.
Find the coordinates of point P.
There are two methods to solve this problem. Choose one to begin: graphing or algebraic.
In triangle ABC, the measure of angle A is 2x+6, the measure of angle B is −4x−3, and the measure of angle C is 9.5x+7. What is the measure of angle C?
How can the triangle angle sum theorem be helpful?
Triangle ABC has vertices A(2,1)A(2, 1)A(2,1), B(6,1)B(6, 1)B(6,1), and C(4,5)C(4, 5)C(4,5). Triangle A′B′C′ is the image of triangle ABC after a sequence of transformations.
Triangle ABC is reflected across the y-axis.
The image is then rotated 90° counterclockwise about the origin.
Finally, the image is dilated with a scale factor of 1/2 centered at the origin.
Determine the coordinates of points A′
Would creating a diagram help?
In the diagram below, triangles △ABC\triangle ABC△ABC and △DEF\triangle DEF△DEF are congruent.
Given:
∠A≅∠D
AB≅DE
AC≅DF
If the measure of ∠B is (4x+10) and the measure of angle E is (6x−14), find the value of x
In right triangle ABC, angle C is a right angle.
Sin (3x+5)=Cos( 5x−25),what is the value of x ?
What do you know about the trig cofunction properties?
In triangle ABC, if AB = 3, BC = 8, and the measure of angle C is 89 degrees, what is the area of triangle ABC?
How can trigonometric functions help us find the area of a triangle when the base and height are not given?