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2 years ago

9

What is the reason for statement 5 in this proof?

3 answers:

Sloan [31]2 years ago

5 0

You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.

kondor19780726 [428]2 years ago

4 0

Answer:

The correct option is D) SAS

Step-by-step explanation:

Consider the provided statement.

SAS Similarity Theorem: If two sides of a triangle are proportional to the two sides of another triangle and the included angle in both are congruent, then the two triangles are similar.

Statement 1: Let ΔABC be an isosceles triangle where AB = BC.

Reason 1: Given

Statement 2: Create point D on so that bisects ∠ABC as shown.

Reason 2: Constructing an angle bisector.

Statement 3: m∠ABD = m∠DBC

Reason 3: Definition of angle bisector

Statement 4: BD = BD

Reason 4: Reflexive Property of Equality

Statement 5: ΔABD ≅ ΔCBD

Reason 5: SAS

Statement 6: m∠BAC = m∠BCA

Reason 6: Corresponding angles of congruent triangles are equal.

From Reflexive Property of Equality we know BD=BD, m∠ABD = m∠DBC definition of angle bisector and AB = BC, which follows the Side angle side (SAS) similarity.

Gavion2 years ago

0 0

What is the reason for statement 5 in this proof?

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Read 2 more answers

1. What are the solutions (coordinate points) to the system of equations?

Leto [7]

Question 1

The given system of equations is:

$y = {x}^{2} + 5x + 6 \\ y = 3x + 6$

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Rewrite in standard form:

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When we put x=-2, into y=3x+6, we get:

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Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

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$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$

The average rate of change is 11

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3 years ago

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erik [133]

Answer:

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