Mathematics, 12.02.2021 18:10 keirarae2005

Prove that the line joining the point of intersection of two angular bisectors of the base angles of an isosceles triangle to the vertex bisects the vertical angle. ~Thanks in advance ! ツ

Answers: 2

Show answers

Answers

Answer from: Ruby2480

See Below.

Step-by-step explanation:

Please refer to the attachment below.

Essentially, we want to prove that AE bisects ∠A.

Statements: Reasons:

$1)\text{ } \Delta ABC \text{ is isosceles}$ Given

$2)\text{ } m\angle C=m\angle B$ Isosceles Triangle Theorem

$3)\text{ }m\angle C=m\angle ACE+m\angle ECD$ Angle Addition

$4)\text{ } CE\text{ bisects }\angle C$ Given

$5)\text{ } m\angle ACE=m\angle ECD$ Definition of Bisector

$6)\text{ } m\angle C=2m\angle ECD$ Substitution

$7)\text{ } m\angle B=\angle ABE+m\angle EBD$ Angle Addition

$8)\text{ } BE\text{ bisects } \angle B$ Given

$9)\text{ }m\angle ABE=m\angle EBD$ Definition of Bisector

$10)\text{ } m\angle B=2m\angle EBD$ Substitution

$11)\text{ } 2m\angle ECD=m\angle EBD$ Substitution

$12)\text{ } m\angle ECD=m\angle EBD$ Division Property of Equality

$13)\text{ } CE=BE$ Isosceles Triangle Theorem

$14)\text{ } AC=AB$ Isosceles Triangle Theorem

$15)\text{ } AE=AE$ Reflexive Property

$16)\text{ } \Delta AEC\cong \Delta AEB$ SSS Congruence

$17)\text{ } \angle CAE\cong \angle BAE$ CPCTC

$18)\text{ } AE\text{ is a bisector of } \angle A$ Converse of Bisector

Prove that the line joining the point of intersection of two angular bisectors of the base angles of

Answer from: taterbug3859

See in the picture above. Hope it would help you out. Have a nice day!

Answer from: Quest

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

Answer from: Quest

Bberodndjxjdjsndndbxhxhxjsjnendbchcjx
Which of the following are equal to the expression? check all that apply

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Which expression is equivalent to the expression below? (6c^2 + 3c) / (-4c + 2) / (2c + 1) / (4c - 1)a. 3c(2c-1) / (2c + 1)b. -3c(2c-1)^2 / (2c + 1)^2c. 3cd. -3c(just took the test its d. -3c)

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

You buy five cds at a sale for $5.95 each. write an expression for the total cost of the cds.then use the distributive property and mental math to evaluate the expression.

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

Harry the hook has 7 1/3 pounds of cookie dough.she uses 3/5 of it to bake cookie. how much cookie dough does she use to make cookie?

Answers: 1

Answer

Mathematics, 22.06.2019 02:30

Adoughnut shop charges $0.50 for each doughnut and $1 for a carryout box. shirley has $10 to spend. which inequality can be used to find d, the number of doughnuts she could have bought if she also wants them in one carryout box?

Answers: 1

Answer

You know the right answer?

Prove that the line joining the point of intersection of two angular bisectors of the base angles of...

Questions