Given: ∠BCD is right; BC ≅ DC; DF ≅ BF; FA ≅ FE Triangles A C D and E C B overlap and intersect at point F. Point B of triangle
E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C D. Line segments B C and C D are congruent. Line segments B F and F D are congruent. Line segments A F and F E are congruent. Which relationships in the diagram are true? Select three options. △ACF ≅ △ECF by HL ΔCBF ≅ ΔCDF by SSS ΔBFA ≅ ΔDFE by SAS ΔCFD ≅ ΔEFD by SSS ΔCBE ≅ ΔCDA by HL
2 answers:
Answer:
1) ΔCBF ≅ ΔCDF by (SSS)
2) ΔBFA ≅ ΔDFE by (SAS)
3) ΔCBE ≅ ΔCDA by (HL)
Step-by-step explanation:
1) Since BC ≅ DC and DF ≅ BF where CF ≅ CF (reflective property) we have;
ΔCBF ≅ ΔCDF by Side Side Side (SSS) rule of congruency
2) Since DF ≅ BF and FA ≅ FE where ∠DFE = ∠BFA (alternate angles)
Therefore;
ΔBFA ≅ ΔDFE by Side Angle Side (SAS) rule of congruency
3) Since FA ≅ FE and DF ≅ BF then where EB = FE + BF and AD = FA + DF
Where:
EB and AD are the hypotenuse sides of ΔCBE and ΔCDA respectively
We have that;
EB = AD from FE + BF = FA + DF
Where we also have BC ≅ DC
Where:
BC and DC are the legs of ΔCBE and ΔCDA respectively
Then we have the following relation;
ΔCBE ≅ ΔCDA by Hypotenuse Leg (HL).
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Answer:
(3)11
Step-by-step explanation:
We are given that
We have to find the sum of positive roots of the equation.
Factor of 336
2,3,4,6,8,7,
Let x=2
x=2 is not the root of equation
x=-2
Hence x=-2 is the root of equation.
x+2 is a factor of equation.
x=3
Therefore, x=3 is the root of equation.
Positive roots are 3 and 8
Sum of positive roots=3+8=11
Option (3) is true.
Answer:
- hexahedron: triangle or quadrilateral or pentagon
- icosahedron: quadrilateral or pentagon
Step-by-step explanation:
<u>Hexahedron</u>
A hexahedron has 6 faces. A <em>regular</em> hexahedron is a cube. 3 square faces meet at each vertex.
If the hexahedron is not regular, depending on how those faces are arranged, a slice near a vertex may intersect 3, 4, or 5 faces. The first attachment shows 3- and 4-edges meeting at a vertex. If those two vertices were merged, then there would be 5 edges meeting at the vertex of the resulting pentagonal pyramid.
A slice near a vertex may create a triangle, quadrilateral, or pentagon.
<u>Icosahedron</u>
An icosahedron has 20 faces. The faces of a <em>regular</em> icosahedron are all equilateral triangles. 5 triangles meet at each vertex.
If the icosahedron is not regular, depending on how the faces are arranged, a slice near the vertex may intersect from 3 to 19 faces.
A slice near a vertex may create a polygon of 3 to 19 sides..
