Question

I'll Mark you brainliest!! I will report answers if you answer for points. Period.

Answer 1

a SAS congruence postulate means that it must have an equal side,angle,side! so in this example, it tells us a side that's equal so you'd need to prove an angle and another side to prove the triangles congruent. I lost my notes on how to solve it sorry.

Answer 2

Answer:

AC is perpendicular to BD.

Step-by-step explanation:

We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that  is reflexive.

The length of the base of the triangle is the same, i.e., .

In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely . Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:  

∠ACB = ∠ACD  

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The following is not other or additional information along with the reasons.  

∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and  

∠BAC = ∠DAC no, because that is ASA with  and ∠ACB = ∠ACD.

No, because already marked.

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Notes:  

The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.

The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.  

The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.

The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.  

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Here's another way to solve it:

Given a triangle ABD.  C is the mid point of BD.

To prove that the two triangles are congruent we have to use SAS axiom.

Here consider two triangles ABC and ADC

Statement                        Reason

1) BC = CD                       D is the mid point of BD

2) AC = AC                       Reflexive property

Since we have two sides congruence we must have included angle congruence

i.e. Angle ACB = Angle ACD

If this information is given, then this completes the SAS congruence for the two triangles ABC and ADC

Hence answer is

the information that AC is perpendicular to BD is sufficient to complete the proof.

Please give me brainliest as you promised you would!