Question

warm up 3
which congruence theorem (sss, sas, asa, or aas) would you use to prove the triangles congruent?
ab = ed
ac = ec
bc = dc
warm up 4
which congruence theorem (sss, sas, asa, or aas) would you use to prove the triangles congruent?
warm up 5
which congruence statement is not true in the following figure?
a. bc ≅ ec
b. ∠acb ≅ ∠ecd
c. ab ≅ de
d. ac ≅ dc
warm up 6
what number do the three interior angles of a triangle always add up to?

Explanation:

Warm Up 3

Step1: Identify given side - side - side equalities

We are given $AB = ED$, $AC=EC$, and $BC = DC$. These are three pairs of corresponding sides.

Step2: Apply congruence theorem

By the SSS (Side - Side - Side) congruence theorem, if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. Answer for Warm Up 3: SSS

Warm Up 4

Step1: Identify side - angle - side information

We have $AB = DE = 7$, $\angle A=\angle E = 60^{\circ}$, and $AC = EF=8$. One pair of sides, the included angles, and another pair of sides are equal.

Step2: Apply congruence theorem

By the SAS (Side - Angle - Side) congruence theorem, the triangles are congruent. Answer for Warm Up 4: SAS

Warm Up 5

Step1: Analyze the congruent triangles

In the figure, we can prove $\triangle ABC\cong\triangle DEC$ by SAS (vertical angles and given side - side equalities).

Step2: Check each option

We know that $AC = DC$, $\angle ACB=\angle ECD$ (vertical angles), and $BC = EC$. Option C ($AB\cong DE$) is not a given or provable fact from the information we have just from the markings. Answer for Warm Up 5: C. $AB\cong DE$

Warm Up 6

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is a well - known geometric fact.

Step2: State the sum

The sum of the three interior angles of a triangle is always $180^{\circ}$. Answer for Warm Up 6: $180^{\circ}$

Answer:

Warm Up 3: SSS
Warm Up 4: SAS
Warm Up 5: C. $AB\cong DE$
Warm Up 6: $180^{\circ}$