Find the surface area of the triangular pyramid

^<br> 6 m<br> 8 m<br> What is the length of the hypotenuse?<br> C =<br> meters

ikadub [295]

Answer:

formula: a squared + b squared= c squared

6 squared+ 8 squared= c squared

36+64= c squared

100= c squared

Square root both sides

You get 10= c

5 0

3 years ago

Charlotte spent 1/2 of the day shopping at all. She spent 1/4 of this time trying on jeans. What fraction of the day did Charlot

RideAnS [48]

Answer:

Charlotte spend $\frac{1}{8}$ of day trying on jeans

Step-by-step explanation:

Charlotte spent part of day on shopping = $\frac{1}{2}$

She spent part of shopping time on trying jeans = $\frac{1}{4}$

We are supposed to find What fraction of the day did Charlotte spend trying on jeans.

She spent fraction of the day in trying jeans = $\frac{1}{2} \times \frac{1}{4}$

She spent fraction of the day in trying jeans = $\frac{1}{8}$

Hence Charlotte spend $\frac{1}{8}$ of day trying on jeans

6 0

3 years ago

1. استخدم ورقة منقطة متساوية القياس لرسم منشور مثلثي بارتفاع 6 وحدات ، وبقاعدتين عبارة عن مثلثين قائمی الزاوية بساقين طولهما 6 و

vladimir2022 [97]

يريدون منك استخدام النقاط لتساعد نفسك في رسم صورة المكعبات. هذا ليس سؤالًا حقًا يمكن لأي شخص مساعدتك في الإجابة عليه حيث عليك فقط رسم الصورة. النقاط هي فقط للمساعدة في جعل الأمر أسهل من مجرد الرسم باليد.

5 0

3 years ago

How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof?

lilavasa [31]

All the theorems are proved as follows.

<h3>What is a Triangle ?</h3>

A triangle is a polygon with three sides , three vertices and three angles.

1. The Triangle sum Theorem

According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.

To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.

We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.

180° - ∠A + 180° - ∠B + 180° - ∠C = 360°

- ∠A - ∠B - ∠C = 360° - (180°+ 180°+ 180°) = -180°

∠A + ∠B + ∠C = 180°

(Hence Proved)

2. Isosceles Triangle Theorem

Considering an isosceles triangle ΔABC

with AB = AC, we have by sine rule;

$\rm \dfrac{sinA}{BC} = \dfrac{sinB}{AC} = \dfrac{sinC}{AB}\\$

as AB = AC

sin B = sin C

angle B = angle C

3.Converse of the Isosceles theorem

Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;

$\rm \dfrac{sinA}{BC} = \dfrac{sinB}{AC} = \dfrac{sinC}{AB}\\$

as ∠B= ∠C ,

AB = AC

4. Midsegment of a triangle theorem

It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.

Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC

In ΔABC and ΔADF

∠A ≅ ∠A

BA = 2 × DA, BC = 2 × FA

Hence;

ΔABC ~ ΔADF (SAS similarity)

BA/DA = BC/FA = DF/AC = 2

Hence AC = 2×DF

5.Concurrency of Medians Theorem

A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and the point of intersection is inside the triangle known as Centroid .

Consider a triangle ABC , X,Y and Z are the midpoints of the sides

Since the medians bisect the segment AB into AZ + ZB

BC into BX + XB

AC into AY + YC

Where:

AZ = ZB

BX = XB

AY = YC

AZ/ZB = BX/XB = AY/YC = 1

AZ/ZB × BX/XB × AY/YC = 1 and

the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).

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