Amy's home is 1.8 km from the shop.
1 answer:
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A Cube, has all equal sides, namely, the length, width and height
are all equal to each other
so.. notice the picture added here
you have really, 6 squares, stacked up to each other at the edges
so...what is the Area of one of those squares?
well, if the sides are equal, let's say the side is "x" long, then
the Area is
well, you have 6 of those squares, thus
solve for "x", to get one side's length
are all equal to each other
so.. notice the picture added here
you have really, 6 squares, stacked up to each other at the edges
so...what is the Area of one of those squares?
well, if the sides are equal, let's say the side is "x" long, then
the Area is
well, you have 6 of those squares, thus
solve for "x", to get one side's length
The right triangles that have an altitude which forms two right triangles
are similar to the two right triangles formed.
Responses:
1. ΔLJK ~ ΔKJM
ΔLJK ~ ΔLKM
ΔKJM ~ ΔLKM
2. ΔYWZ ~ ΔZWX
ΔYWZ ~ ΔYZW
ΔZWX ~ ΔYZW
3. x = <u>4.8</u>
4. x ≈ <u>14.48</u>
5. x ≈ <u>11.37</u>
6. G.M. = <u>12·√3</u>
7. G.M. = <u>6·√5</u>
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<h3>What condition guarantees the similarity of the right triangles?</h3>1. ∠LMK = 90° given
∠JMK + ∠LMK = 180° linear pair angles
∠JMK = 180° - 90° = 90°
∠JKL ≅ ∠JMK All 90° angles are congruent
∠LJK ≅ ∠LJK reflexive property
- <u>ΔLJK is similar to ΔKJM</u> by Angle–Angle, AA, similarity postulate
∠JLK ≅ ∠JLK by reflexive property
- <u>ΔLJK is similar to ΔLKM</u> by AA similarity
By the property of equality for triangles that have equal interior angles, we have;
- <u>ΔKJM ~ ΔLKM</u>
2. ∠YWZ ≅ ∠YWZ by reflexive property
∠WXZ ≅ ∠YZW all 90° angle are congruent
- <u>ΔYWZ is similar to ΔZWX</u>, by AA similarity postulate
∠XYZ ≅ ∠WYZ by reflexive property
∠YXZ ≅ ∠YZW all 90° are congruent
- <u>ΔYWZ is similar to ΔYZW</u> by AA similarity postulate
Therefore;
- <u>ΔZWX ~ ΔYZW</u>
3. The ratio of corresponding sides in similar triangles are equal
From the similar triangles, we have;
8 × 6 = 10 × x
48 = 10·x
3. From the similar triangles, we have;
20 × 21 = x × 29
420 = 29·x
4. From the similar triangles, we have;
20 × 48 = 52 × x
5. From the similar triangles, we have;
13.2 × 22.4 = 26 × x
6. The geometric mean, G.M. is given by the formula;
The geometric mean of 16 and 27 is therefore;
- The geometric mean of 16 and 27 is <u>12·√3</u>
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7. The geometric mean of 5 and 36 is found as follows;
- The geometric mean of 5 and 36 is <u>6·√5</u>
Learn more about the AA similarity postulate and geometric mean here:
