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4 years ago

Assemble the proof by dragging tiles to the statements HELLPPPPPP PLEASEEEE

Mathematics

2 answers:

TEA [102]4 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

1. $JK\cong LM$ - given

2. $JL\cong LN$ - definition of midpoint (the midpoint of the segment divides the segment into two congruent segments)

3. $\angle LJK\cong \angle NLM$ - corresponding angles theorem (corresponding angles theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.)

4. $\triangle JLK\cong \triangle LNM$ - SAS (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).

solong [7]4 years ago

6 0

Step-by-step explanation:

Triangle Congruence :SAS

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3 years ago

Several paint mixtures are made by mixing blue paint and white paint. Paint Colors Blue Paint White Paint Mixture A 5 cups 12 cu

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Answer:

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Step-by-step explanation:

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3 years ago

In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .