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

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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

well my understanding of this question is they want you to use the y=14.1x -2.3 and put the coordinates they gave you onto the line segment of y=14.1x -2.3

step-by-step explanation:

Answer from: Quest

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

$\frac{48}{4}$ = 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

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