Are the triangles congruent?
Classifying triangles and congruency statements
Review
100
Are the triangles congruent? Explain
No. SSA can form two triangles, so not guaranteed congruent.
100
Classify the triangles by sides and angles, explain:
Since no sides congruent and all angles less than 90 degrees, this is an acute scalene triangle.
100
If the two lines are parallel are
angle2congangle6
.Explain. 
Yes they are congruent since corresponding angles are congruent when lines parallel.
200
Are the following congruent? Explain
Yes. Since both triangles are right triangles, have a leg congruent, and share there hypotenuse (so congruent). The two triangles would be congruent by Hypotenuse Leg Congruency.
200
Draw an example of a obtuse equilateral triangle
cannot! equilateral has all 60 degree angles (always acute)
200
Find a line that is parallel and another line perpendicular to
y=2x-75
that goes through the point (-2,3)
Parallel: y=2x+7
Perpendicular: y=-1/2x+2
300
Are the two triangles congruent? Explain:
Yes. Since they have a pair of parallel sides, we can say angleBcongangleC since alternate interior angles congruent when lines parallel. Also, angleBXAcongangleCXD since fertical angles are congruent. So the two triangles congruent by Angle Angle Side congruency.
300
Given
triangleZYWcongtriangleXER
State all congruent parts and draw a diagram.
Congruent parts:
angleZcongangleX
angleYcongangleE
angleWcongangleR
ZYcongXE
YWcongER
ZWcongXR
300
Solve for x:
x=12
400
Are the triangles congruent if both
triangleJZF
and
triangleQZX
are isosceles? Explain:
Yes, since isosceles angleJcongangleF since base angles are congruent and JZcongFZ by definition of isosceles. Also since angleZQXcongangleZXQ we know that angle1congangle2 since they are both linear pairs with angleZQX and angleZXQ . So by Angle Angle Side congruency the triangles are congruent.
400
If
triangleABCcongtriangleDEF
mangleD=20
mangleF=70
"Find":mangleB
"Then find": AC if BC=3 and AB=4
Since congruent triangles have congruent corresponding parts mangleB=mangleE=90 . So since ABC is a right triangle, use pythagoreans theorem to find AC=5
400
Factor the quadratic:
7x^2 -13x-2
(7x+1)(x-2)
500
Given
triangleABC
is isosceles. Is
triangleKK'McongtriangleLL'M
? Explain:
by Angle Side Angle Congruency
500
Create a coordinate proof:
()
500
Perform the following transformations on A(1,1), B(-2,-1), and C(5,-2):
1. Reflection over y=x
2. Rotation 90 degrees CCW about the origin
3. Dilation about the origin by a factor of 3
Answer