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Consider isosceles triangle ABC with angle bisector AD¯¯. What reasons complete the proof of ∠B≅∠C?  Drag the phrases to the empty boxes to correctly complete each sentence of the proof. AB¯¯≅AC¯¯ because -  ∠BAD≅∠CAD because - AD¯¯≅AD¯ because - △ABD≅△ACD because - ∠B≅∠C because -  Answer choices : of AAS ; of ASA ; of SSS ; it is given ; of the reflexive property ; of the definition of angle bisector ;

Consider isosceles triangle ABC with angle bisector AD¯¯. What reasons complete the proof of ∠B≅∠C?  Drag the phrases to the empty boxes to correctly complete each sentence of the proof. AB¯¯≅AC¯¯ because -  ∠BAD≅∠CAD because - AD¯¯≅AD¯ because - △ABD≅△ACD because - ∠B≅∠C because -  Answer choices : of AAS ; of ASA ; of SSS ; it is given ; of the reflexive property ; of the definition of angle bisector ;

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 14E
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Consider isosceles triangle ABC with angle bisector AD¯¯.

What reasons complete the proof of ∠B≅∠C?  Drag the phrases to the empty boxes to correctly complete each sentence of the proof.

AB¯¯≅AC¯¯ because - 

∠BAD≅∠CAD because -

AD¯¯≅AD¯ because -

△ABD≅△ACD because -

∠B≅∠C because - 

Answer choices : of AAS ; of ASA ; of SSS ; it is given ; of the reflexive property ; of the definition of angle bisector ; corresponding parts of congruent triangles are congruent. 

A В D C
Transcribed Image Text:A В D C
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# Proof of Congruent Angles in an Isosceles Triangle ## Consider isosceles triangle \( \triangle ABC \) with angle bisector \( AD \). ![Isosceles Triangle with Angle Bisector](...insert_image_source_here...) ### Given: - Triangle \( \triangle ABC \) is isosceles with \( AB = AC \) - \( AD \) is the angle bisector of \( \angle BAC \) ### What reasons complete the proof of \( \angle ABD \cong \angle ACD \)? Drag the phrases to the empty boxes to correctly complete each sentence of the proof. 1. \( \overline{AB} \cong \overline{AC} \) because _______________. 2. \( \angle BAD \cong \angle CAD \) because _______________. 3. \( \overline{AD} \cong \overline{AD} \) because _______________. 4. \( \triangle ABD \cong \triangle ACD \) because _______________. 5. \( \angle B \cong \angle C \) because _______________. ### Phrases to choose from: - of AAS - of ASA - of SAS - of SSS - it is given - of the reflexive property - of the definition of angle bisector - corresponding parts of congruent triangles are congruent ### Graph Description: The graph shows an isosceles triangle \( \triangle ABC \) with \( AB \) congruent to \( AC \), and \( AD \) bisecting \( \angle BAC \), meeting \( BC \) at point \( D \). ### Step-by-Step Solution: 1. \( \overline{AB} \cong \overline{AC} \) because **it is given**. 2. \( \angle BAD \cong \angle CAD \) because **of the definition of angle bisector**. 3. \( \overline{AD} \cong \overline{AD} \) because **of the reflexive property**. 4. \( \triangle ABD \cong \triangle ACD \) because **of SAS**. 5. \( \angle B \cong \angle C \) because **corresponding parts of congruent triangles are congruent**. Understanding this proof helps in mastering the concept of congruence
Transcribed Image Text:# Proof of Congruent Angles in an Isosceles Triangle ## Consider isosceles triangle \( \triangle ABC \) with angle bisector \( AD \). ![Isosceles Triangle with Angle Bisector](...insert_image_source_here...) ### Given: - Triangle \( \triangle ABC \) is isosceles with \( AB = AC \) - \( AD \) is the angle bisector of \( \angle BAC \) ### What reasons complete the proof of \( \angle ABD \cong \angle ACD \)? Drag the phrases to the empty boxes to correctly complete each sentence of the proof. 1. \( \overline{AB} \cong \overline{AC} \) because _______________. 2. \( \angle BAD \cong \angle CAD \) because _______________. 3. \( \overline{AD} \cong \overline{AD} \) because _______________. 4. \( \triangle ABD \cong \triangle ACD \) because _______________. 5. \( \angle B \cong \angle C \) because _______________. ### Phrases to choose from: - of AAS - of ASA - of SAS - of SSS - it is given - of the reflexive property - of the definition of angle bisector - corresponding parts of congruent triangles are congruent ### Graph Description: The graph shows an isosceles triangle \( \triangle ABC \) with \( AB \) congruent to \( AC \), and \( AD \) bisecting \( \angle BAC \), meeting \( BC \) at point \( D \). ### Step-by-Step Solution: 1. \( \overline{AB} \cong \overline{AC} \) because **it is given**. 2. \( \angle BAD \cong \angle CAD \) because **of the definition of angle bisector**. 3. \( \overline{AD} \cong \overline{AD} \) because **of the reflexive property**. 4. \( \triangle ABD \cong \triangle ACD \) because **of SAS**. 5. \( \angle B \cong \angle C \) because **corresponding parts of congruent triangles are congruent**. Understanding this proof helps in mastering the concept of congruence
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