5.6 PROVING TRIANGLE CONGRUENCE BY ASA AND AAS SOFTWARE

By the Third Angles Theorem (Theorem 5.4), Section 5.6 Proving Triangle Congruence by ASA and AAS 271Īngle-Angle-Side (AAS) Congruence Theorem Using the ASA and AAS Congruence Theorems What You Will LearnWhat You Will Learn Use the ASA and AAS Congruence Theorems. The included side of a second triangle, then the two triangles are congruent. TheoremTheoremTheorem 5.10 Angle-Side-Angle (ASA) Congruence TheoremIf two angles and the included side of one triangle are congruent to two angles and So, this refl ection maps △DB″F to △DEF.īecause you can map △ABC to △DEF using a composition of rigid motions, Because ��⃗ DE and ��⃗ FE only have point E in common, the image ofī″ must be E. The image ofī″ lies on ��⃗ DE and ��⃗ FE. Similarly, because ∠B″FD ≅ ∠EFD, the refl ection maps ��⃗ FB″ to ��⃗ FE. BecauseĪ refl ection preserves angle measure and ∠B″DF ≅ ∠EDF, the refl ection maps ��⃗ DB″ to Now, refl ect △DB″F in the line through points D and F, asīecause points D and F lie on ⃖ ��⃗ DF, this refl ection maps them onto themselves. Through ∠C′DF so that the image of ��⃗ DC′ coincides with ��⃗ DF, as shown below.īecause - DC′ ≅ - DF, the rotation maps point C′ to point F. To be profi cient in math, you need to recognize and use counterexamples.Įssential QuestionEssential Question What information is suffi cient to determineĥ.6 Proving Triangle Congruenceby ASA and AASĪngle-Side-Angle (ASA) Congruence Theoremįirst, translate △ABC so that point A maps to point D, as shown below. Is it possible to show that two triangles are congruent using more than oneĬongruence theorem? If so, give an example. What information is suffi cient to determine whether two triangles are congruent?Ĥ. Possible Congruence Theorem Valid or not valid?Ĭommunicate Your AnswerCommunicate Your Answer 3. For those that are not valid, writeĪ counterexample.

5.6 PROVING TRIANGLE CONGRUENCE BY ASA AND AAS SOFTWARE

Use dynamic geometry software to determine which of theįollowing are valid triangle congruence theorems. Is SSA suffi cient to determine whether two triangles are congruent? Explain Is △ABC ≅ △ABD? Explain your reasoning.Į. △ABC and △ABD have two congruent sides and a nonincluded congruent angle.ĭ. Locate point Dwhere the circle intersects -AC. Construct a circle with a radius of 2 units centered at the origin. Vertex B is at the origin, -AB has a length of 3 units, and -BC has a length of 2 units.ī. Use dynamic geometry software to construct △ABC. Section 5.6 Proving Triangle Congruence by ASA and AAS 269Ī. Essential Question Essential Question What information is sufﬁcient to determine whether two triangles are congruent? 5.6 Proving Triangle Congruence by ASA and AAS CONSTRUCTING VIABLE ARGUMENTS To be proﬁcient in math, you need to recognize and use counterexamples. Is it possible to show that two triangles are congruent using more than one congruence theorem? If so, give an example. What information is sufﬁcient to determine whether two triangles are congruent? 4. Possible Congruence Theorem Valid or not valid? SSS SSA SAS AAS ASA AAA Communicate Your Answer Communicate Your Answer 3.

For those that are not valid, write a counterexample. Use dynamic geometry software to determine which of the following are valid triangle congruence theorems.

Determining Valid Congruence Theorems Work with a partner. Is SSA sufﬁcient to determine whether two triangles are congruent? Explain your reasoning. Is △ ABC ≅ △ ABD ? Explain your reasoning. △ ABC and △ ABD have two congruent sides and a nonincluded congruent angle. Locate point D where the circle intersects - AC.

Construct the triangle so that vertex B is at the origin, - AB has a length of 3 units, and - BC has a length of 2 units. Use dynamic geometry software to construct △ ABC. Section 5.6 Proving Triangle Congruence by ASA and AAS 269 Learning Standard HSG-CO.B.8 C OMMON C ORE Determining Whether SSA Is Sufﬁcient Work with a partner.

5.6 proving triangle congruence by asa and aas