To determine if triangle ABC and triangle AED are congruent, we need to compare their corresponding sides and angles.
Looking at their corresponding sides:
1) Side AB is congruent to side AE (given).
2) Side BC is congruent to side ED (given).
3) Side AC is congruent to side AD (given).
All three pairs of corresponding sides are congruent.
Now, let's examine their corresponding angles:
1) Angle A is congruent to angle A (reflexive property).
2) Angle B is congruent to angle E (alternate interior angles, given).
3) Angle C is congruent to angle D (alternate interior angles, given).
All three pairs of corresponding angles are congruent.
Since all corresponding sides and angles of triangle ABC and triangle AED are congruent, we can conclude that the triangles are congruent by the Side-Angle-Side (SAS) congruence criterion.
Note: Your teacher will grade your responses to questions 7–10 to ensure you receive proper credit for your answers.
State whether triangleABC and triangleAED are congruent. Justify your answer.
4 answers
show me the the answer from chegg com regarding this question
I apologize, but I don't have access to Chegg.com answers. However, here is an example response for your reference:
"To determine if triangle ABC and triangle AED are congruent, we can use the Side-Angle-Side (SAS) congruence criterion.
For side AB and AE, it is given that AB = AE.
For side BC and ED, it is given that BC = ED.
For side AC and AD, it is given that AC = AD.
So, all three pairs of corresponding sides are congruent.
Now let's examine the angles.
Angle A is congruent to angle A by the reflexive property.
Angle B is congruent to angle E, as they are alternate interior angles (given).
Angle C is congruent to angle D, also as alternate interior angles (given).
Therefore, all three pairs of corresponding angles are congruent as well.
Since all corresponding sides and angles are congruent, we can conclude that triangle ABC and triangle AED are congruent by the SAS congruence criterion."
Remember, it's always important to understand and explain the reasoning behind the answer rather than simply copying it, in order to demonstrate your own comprehension of the concept.
"To determine if triangle ABC and triangle AED are congruent, we can use the Side-Angle-Side (SAS) congruence criterion.
For side AB and AE, it is given that AB = AE.
For side BC and ED, it is given that BC = ED.
For side AC and AD, it is given that AC = AD.
So, all three pairs of corresponding sides are congruent.
Now let's examine the angles.
Angle A is congruent to angle A by the reflexive property.
Angle B is congruent to angle E, as they are alternate interior angles (given).
Angle C is congruent to angle D, also as alternate interior angles (given).
Therefore, all three pairs of corresponding angles are congruent as well.
Since all corresponding sides and angles are congruent, we can conclude that triangle ABC and triangle AED are congruent by the SAS congruence criterion."
Remember, it's always important to understand and explain the reasoning behind the answer rather than simply copying it, in order to demonstrate your own comprehension of the concept.
Which answer is correct?