Step-by-step explanation:
I'll do the first problem as an example.
∠P and ∠H both have one mark. That means they're congruent.
∠T and ∠G both have two marks. So they're congruent.
∠W and ∠D both have three marks. So they're congruent.
So we can write a congruence statement:
ΔPTW ≅ ΔHGD
We can write more congruence statements by rearranging the letter, provided that corresponding pairs have the same position (P is in the same place as H, etc.). For example:
ΔWPT ≅ ΔDHG
ΔTWP ≅ ΔGDH
1 hiker left the trail while 1 is still on it, so theres 1 hiker on the trail.
Prime factorize the two numbers:
666 = 2 x 3 x 3 x 37
888 = 2 x 2 x 2 x 3 x 37
Notice I lined up all the numbers into columns. If they appear for both numbers they are paired. The lowest common multiple is the product of all the unique columns:
LCM = 2 x 2 x 2 x 3 x 3 x 37 = 2664
You can use this strategy for as many numbers as you want. Also, you could find the greatest common factor by multiplying only the paired columns.
532.60
x 8.53
--------------------------------
159780
+ 2663000
42608000
---------------------------
4543.0780
For the first one, divide the figure into shapes you know how to use. This one can be turned into 2 rectangles and 1 square. Find the area (length*width) of each new shape and add them together. For example the rectangles would have an area that is 31*23 or 713 m.
For the second one do the same. It is 1 rectangle and 2 triangles. The area of a rectangle (length*width) in this case would be 24*8 or 192 cm and the area of the triangles are 1/2*base*height (you need to use the Pythagorean theorem to find the other length of the triangle) and add up the areas to get the total.
To find the surface area of the last one, there are 6 sides. The area of two of the sides are 15*4. Two of the sides are 15*3. The last two sides are 4*3. Add the areas up to find the total surface area.
Hope this helps! :)
