Mathematics, 28.12.2019 06:31 zulfiquer5541

Match the reasons with the statements given.
prove theorem 4-22
(hint: show adb cdb.)

given:
abcd is rhombus
prove: db bisects abc and adc

abcd is a rhombus
given
2. triangle adb congruent to triangle cdb
definition of angle bisector.
3. ∠1 = ∠2, ∠3 = ∠4
cpcte
4. db bisects ∠abc and ∠adc
diagonals of parallelogram make congruent triangles.

Match the reasons with the statements given. prove theorem 4-22 (hint: show adb cdb.)

Answers: 1

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Answers

Answer from: dondre54

I believe the matching would be as follows;
1. ABCD is a rhombus -Given
2. Triangle ADB congruent to Triangle CDB- Diagonals of parallelogram make congruent triangles. The two triangles share a diagonal BD as their third side.
3. ∠1=∠2, ∠3=∠4 ; CPCTE
4. DB bisects ∠ABC and ∠ADC - definition of angle bisector

Answer from: jonathanrgarcia

Given: ABCD is a rhombus

To prove: DB bisects ∠ABC and ∠ADC (∠1=∠2 and ∠3=∠4)

Proof: In ΔADB and ΔCDB

AD=CD (sides of same rhombus)

DB=DB (common in both triangle)

AB=CB (sides of same rhombus)

∴ ΔADB ≅ ΔCDB by SSS congruence property.

Angle bisector: A line divide an angle into two equal part.

CPCT: Congruent part of congruence triangles.

Match the statements:-

ABCD is rhombus ⇒ Given ΔADB≅ΔCDB ⇒ Diagonals of parallelogram make congruent Δ ∠1=∠2,∠3=∠4 ⇒ CPCTE DB bisects ∠ABC and ∠ADC ⇒ Definition of angle bisector

Thus, Above matching is correct.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is