Triangle Congruence: SAS

Question 1

To show that ΔFGH ≅ ΔJKL by SAS, what additional information is needed? Check all that apply.

Revolt · Accepted Answer

FH ≅ JL and FG ≅ JK; FH ≅ JL and HG ≅ LK

Question 2

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

Rigid transformations preserve segment lengths and angle measures.; A rigid transformation, or a combination of rigid transformations, will produce congruent figures.; In proving SAS, we started with two triangles that had a pair of congruent corresponding sides and congruent corresponding included angles.; We mapped one triangle onto the other by a translation, followed by a rotation, followed by a reflection, to show that the triangles are congruent.

Question 3

Complete the missing parts of the paragraph proof.

Revolt · Accepted Answer

✔ it is given; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: it is given; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: RQS; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: the reflexive property; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: SAS

Question 4

QSR✔ RQSSRQ

Revolt · Accepted Answer

✔ RQS

Question 5

SASthe definition of angle bisector✔ the reflexive property

Revolt · Accepted Answer

✔ the reflexive property

Question 6

✔ SASthe definition of angle bisectorthe reflexive property

Revolt · Accepted Answer

✔ SAS

Question 7

How are rigid transformations used to justify the SAS congruence theorem?

Revolt · Accepted Answer

Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.

Question 8

Which pair of triangles can be proven congruent by SAS?

Revolt · Accepted Answer

[Image: 2 triangles are shown. The first triangle is rotat...]

Question 9

To show that ΔFGH ≅ ΔJKL by SAS, what additional information is needed? Check all that apply.

Revolt · Accepted Answer

FH ≅ JL and FG ≅ JK; FH ≅ JL and HG ≅ LK

Question 10

Complete the missing parts of the paragraph proof.

Revolt · Accepted Answer

We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: it is given; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: RQS; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: the reflexive property; We know that segment QS bisects angle TQR because . By the definition of angle bisector, angle TQS is congruent to angle . We see that segment QS is congruent to segment SQ by . Therefore, we can conc: SAS

Triangle Congruence: SAS Answers

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