Triangles and Angles
Congruence and Triangles
SSS, SAS, ASA, AAS
Isosceles, Equilateral, and Right Triangles
Using Congruent Triangles
100
What is the hypotenuse?
The side opposite of the right angle.
100
Which angles are corresponding angles?Angles 1 & 5
Angles 4 & 8
Angles 2 & 6
Angles 3 & 7
100
Would these triangles be considered congruent if you use AAS?Yes.
100
What is the definition of an isosceles triangle?
A triangle with at least two congruent sides.
100
What does HL stand for?
Hypotenuse Leg
200
If a triangle has two congruent sides and an angle that measures ninety degrees, what kind of triangle is it?
It is a right isosceles triangle.
200
Write a congruence statement for the two triangles.200
Given: BA is parallel to DE, AC≅CD, ∠BAC≅∠EDC
Prove: ΔBAC≅ΔEDC
Use a paragraph proof.It is given that BA is parallel to DE, AC≅CD, and ∠BAC≅∠EDC. Use reflexive to prove that ∠C≅∠C. (Answer may vary, possibly using alternate exterior angle.) So ΔBAC≅ΔEDC by ASA.
200
How do you prove angle B is congruent to angle C?The base angles theorem.
200
What does CPCTC stand for?
Corresponding parts of congruent triangles are congruent.
300
If a triangle has equiangular angles, then what are the angle measures and what type of triangle is it?
60 degrees and equiangular equilateral
300
There are two triangles. Triangle TOP and triangle GUN. If angle T is congruent to angle G and angle P is congruent to angle N, how do you prove angle O is congruent to angle U?
Third Angles Theorem
300
Is it possible to prove these triangles congruent? If so, how?Yes, SSS
300
Is an equilateral triangle also considered an isosceles triangle?
Yes.
300
If CPCTC applies to these two triangles, write a congruence statement for the sides of the triangles ONLY.AC≅EG
CB≅GF
BA≅FE
400
Measure of angle X=60
Measure of angle Y=40
What are the measures of the missing angles?
Measure of angle W=100
Measure of angle Z=80
400
Triangle LMN is congruent to Triangle PQR, and the measure of angle L is 105°, and the measure of angle Q is 45°. What are the missing angle measures?
P=105°
M=45°
N=30°
R=30°
400
Are these triangles congruent?NO!
400
What are the measure of the angles in a regular right isosceles triangle?
90 degrees, 45 degrees, 45 degrees
400
Can you prove two triangles congruent if 3 corresponding angles are congruent?
NO
500
If triangle ABC is a right triangle and measure of angle ABC=42 and measure of angle BCA=90, then what is the measure of angle CBA?
48 degrees
500
According to Theorem 4.4, what are the properties of congruent triangles?
Reflexive Property of Congruent Triangles
Symmetric Property of Congruent Triangles
Transitive Property of Congruent Triangles
500
Given: JK is congruent to NK
A is the midpoint of JN
Prove: Triangle JAK is congruent to triangle NAK
1)JK is congruent to NK, A is the midpoint of JN (GIVEN)
2)JA is congruent AN (Definition of midpoint)
3)AK is congruent AK (Reflexive)
4)Triangle JAK is congruent to triangle NAK (SSS)
500
What is the Pythagorean Theorem, and what does it apply to?
a^2+ b^2=c^2, right triangles.
500
If two corresponding sides are congruent and they surround two corresponding vertical angles, what would you use to prove these triangles congruent?
The SAS congruence theorem
(SAS)