Proving Triangles are
Congruent
Classifying Triangles and Their Parts
Theorems
Proofs:
(Please pretend that all similarity symbols are congruent symbols)
Using Definition of Congruent Figures
100
Are these triangles congruent? Why or why not?
Yes; ASA.
100
A triangle with no congruent sides
What is a scalene triangle?
100
A theorem that states that the measures of all interior angles of a triangle add up to 180˚.
What is the triangle sum theorem?
100
Given: AB≅BD, Triangles ABC and DBC are right triangles; Prove: Triangle ABC≅ Triangle DBC
100
What's the measure of angle R? Given: Triangle GCF is congruent Triangle QPR
m∠R=42
200
Are these triangles congruent? Why or why not? Given: ∠F≅∠N
No; there is no booty in math.
200
Classify this triangle by its angles and sides.
It is a right isosceles triangle.
200
A theorem that says that if two sides of a triangle are congruent, then the angles opposite them are congruent. The converse is if two of a triangle's interior angles are congruent, then the sides opposite them are congruent.
What is base angles theorem and its converse?
200
Given: Segment AD// Segment EC, Segment BD≅ Segment BC; Prove: Triangle ABD≅ Triangle EBC
200
What's measure of angle D? Given: Triangle CAS is congruent to Triangle DEN
m∠D=40
300
Are these triangles congruent? Why or why not?
No; AAA only proves similarity.
300
The sides that form the right angle in a right triangle
What are legs?
300
A theorem that states that the measure of an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
What is the exterior angles theorem?
300
Fill in the blanks. Given: B is the midpoint of segment AD, ∠C≅∠E, and BC//DE. Prove: ∠BAC≅∠DBE
2) Definition of midpoint 4) Corresponding angles theorem 5) Triangle BED≅ Triangle ACB 6) CPCTC
300
Find x. Given: Triangle ORN is congruent to Triangle KPL.
x=19
400
Are these these triangles congruent? Why or why not?
Yes; ASA.
400
Classify this triangle by its angles and its sides.
It is an equiangular equilateral triangle.
400
A theorem that says that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
What is third angles theorem?
400
Given: N is midpoint of Segment RE, N is the midpoint of Segment IL Prove: Segment RI//Segment LE
400
What's the measure of angle M? Given: Triangle DIM congruent Triangle FOR
m∠M=80
500
Are these triangles congruent? Why or why not?
Yes; AAS.
500
Classify this triangle by its angles and its sides.
It is an obtuse scalene.
500
x=50˚ y=80˚ Base angles theorem and triangle sum theorem
500
The theorem explained in this proof is _________. Given: ∠A≅∠D, ∠B≅∠E; Prove: ∠C≅∠F
The third angles theorem.
500
What is the congruence statement, why, and what is Segment BD congruent to? Given: Segment AB // Segment EC, Segment is AD congruent to Segment CD
Triangle ABD is congruent to Triangle CED; AAS; Segment DE.
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