Explanation:
1. ∠BAC≅∠BCA, ∠ABD≅∠ADB; Reason: definition of isosceles triangles
2. ∠ABD +∠BAC +∠ADB = 180°; Reason: sum of internal angles is 180°
3. ∠BAC = 180° -2(∠ABD) = 36°; Reason: Subtraction and substitution properties of equality
4. ∠BAC +∠BCA +∠ABC = 180°; Reason: sum of internal angles is 180°
5. ∠BCA = 180° -2(∠BAC) = 108°; Reason: Subtraction and substitution properties of equality
6. ∠ABD +∠DBC = ∠ABC; Reason: Angle sum theorem
7. ∠DBC = ∠ABC -∠ABD = 108° -72° = 36°; Reason: Subtraction and substitution properties of equality
8. ∠BCA = ∠BAC = 36°; Reason: Substitution property of congruence
9. ΔBCD is isosceles; Reason: Base angles DBC and BCA are congruent.
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There may be extra steps involved if you separately use subtraction and substitution properties of equality, or if you separately claim congruence of angles and equality of their measures. We have assumed that the definition of "isosceles triangle" includes the fact of equal side lengths <u>and</u> equal base angles.
Given:
The equation is:
A model with 3 rows of 8 and 3 rows of 4.
To find:
The missing value in Ming's equation.
Solution:
We have,
...(i)
A model with 3 rows of 8 and 3 rows of 4. Using this information, we get
Taking out the common factor 3, we get
...(ii)
On comparing (i) and (ii), we get the missing value is 3.
Therefore, the missing value in Ming's equation is 3.
Yes that's right - that means that if you take one triangle and multiply all its sides by the SAME factor, you'll end up with the other triangle. It's the same shape, just a different size.
Answer:
<h3>
x = 5 units</h3>
Step-by-step explanation:
area of a triangle = 1/2 base * height
where area = 10 units²
height = x units
base = 4
<u>plugin values into the formula:</u>
10 = 1/2 * 4 * x
x =<u> 10 (2) </u>
4
x = 5 units
