Using Triangle Congruence Theorems Answers

Which congruency theorem can be used to prove that △ABD ≅ △DCA?

SSS✔ HLSAS AAS

ASA✔ SAS AAS SSS

We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then determine △ABC ≅ △AED by [___]. Because of CPCTC, segment AC is congruent to segment [___]. Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.

SASASA AAS CPCTC

SAS ASA AAS✔ CPCTC

Analyze the figure and the two-column proof.

ASA AAS✔ HL SAS

SSS HLSAS AAS

Which congruency theorem can be used to prove that △GHL ≅ △KHJ?

Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof? Triangles A C D and E C B are shown. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C B. Angles C A D and B E C are congruent. The lengths of line segments A B and D E are congruent. The lengths of line segments B C and C D are congruent.

Mikal is proving that AE ≅ CE . Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent. Which reason does the ♣ represent in Mikal’s proof?

Which congruency theorem can be used to prove that △ABD ≅ △DCA?

Which congruency theorem can be used to prove that △GHL ≅ △KHJ?

Which statements regarding the diagram are correct? Check all that apply.

Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof? Triangles A C D and E C B are shown. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C B. Angles C A D and B E C are congruent. The lengths of line segments A B and D E are congruent. The lengths of line segments B C and C D are congruent.

Mikal is proving that AE ≅ CE . Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent. Which reason does the ♣ represent in Mikal’s proof?

We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then determine △ABC ≅ △AED by [___]. Because of CPCTC, segment AC is congruent to segment [___]. Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.

Complete the paragraph proof: