supplementary angles
🎯 there is theorem 1:
two supplementary angles. one are greater 3 two.
are angles?
Explanation: See the definition and relevant formula above.
❓ theorem:
α -β supplementary angles, -α = 110°,
β to be 70°?
💡 : 1: given? 🔍 🔹 α -β supplementary angles
🔹 α = 110°
🔹 : β to be 70°? |
2: theorem 📐
📐 theorem 2:
vertical angles _____ each other.
Explanation: See the definition and relevant formula above.
🎯 there is theorem 2:
two because. one angles is 65°.
angle ?
💡 : 1: given? 🔍 🔹 two because
🔹 angle one = 65°
🔹 : angle |
2: theorem 📐
🎯 there is theorem 2:
two because. one angles is 3x+15°.
angle is 75°.
x?
💡 : 1: given? 🔍 🔹 angle 1 = 3x + 15°
🔹 angle 2 () = 75°
🔹 : x = ? |
2: theorem 📐 vertical ang
🎯 theorem 1 -2:
two because 4 angles.
one angles is 40°, angles 140° there is?
💡 : 1: 🔍 🔹 two because → 4 angles
🔹 one angles = 40°
🔹 : angles 140° there is/has? |
2: theorem 2 💭 theorem 2: vertical angles equal
there is/has angle 40°
📐 theorem 3:
triangle, opposite equal angles _____ equal.
💡 : 1: theorem 🔍 theorem 3 ✨ triangle,
opposite equal angles
sides equal
🎯 there is theorem 3:
triangle ABC, angle A = angle B = 65°.
the side BC = 8 cm, the side AC?
💡 : 1: given? 🔍 🔹 triangle ABC
🔹 ∠A = ∠B = 65° (equal angles!)
🔹 BC = 8 cm
🔹 : AC = ? |
2: opposite angle? 💭 | angle | the s
🎯 there is theorem 3:
triangle, two equal angles. the side opposite angle is 2x+3.
the side opposite angle two is 11 cm. x?
💡 : 1: given? 🔍 🔹 two angles equal triangle
🔹 1 (opposite angle 1) = 2x + 3
🔹 2 (opposite angle 2) = 11 cm
🔹 : x = ? |
2: theorem 📐
❓ theorem:
triangle ABC, ∠A = 70° -∠B = 70°.
necessarily AC = BC?
💡 : 1: given? 🔍 🔹 ∠A = 70°
🔹 ∠B = 70°
🔹 : necessarily AC = BC? |
2: sides opposite angles 💭 | angle | the side opposite |
📐 theorem 4:
isosceles triangle, angles _____ equal each other.
💡 : 1: isosceles triangle? 🔍 isosceles triangle triangle two sides equal
the side equal : ""
the side there is/has : ""
🎯 there is theorem 4:
triangle ABC isosceles (AB = AC), angle B = 55°.
angle C?
Explanation: See the definition and relevant formula above.
🎯 there is theorem 4:
isosceles triangle, base angles are 40° every one.
angle ?
💡 : 1: given? 🔍 🔹 triangle isosceles
🔹 base angles = 40° all/every one
🔹 : angle = ? |
2: theorem 💭
❓ theorem:
triangle ABC, AB = AC,
∠B to be equal for ∠C?
💡 : 1: given? 🔍 🔹 AB = AC (two sides equal)
🔹 : necessarily ∠B = ∠C? |
2: triangle 💭 AB = AC → two sides equal
triangle is/it is
🎯 there is theorem 4:
isosceles triangle, angle one is 2x+10°.
angle two is 50°. x?
💡 : 1: given? 🔍 🔹 triangle isosceles
🔹 angle 1 = 2x + 10°
🔹 angle 2 = 50°
🔹 : x = ? |
2: theorem 📐
📐 theorem 5:
every two sides triangle _____ the side there is.
💡 : 1: theorem 🔍 theorem 5 ✨ all/every two sides triangle
greater/larger
the side there is/has
🎯 there is theorem 5:
can be triangle sides: 3, 4, 8?
💡 : 1: given? 🔍 🔹 three sides: 3, 4, 8
🔹 : can to be triangle? |
2: theorem 📐 theorem 5:
all/every two sides
🎯 there is theorem 5:
triangle, two sides are 5 -12.
there is?
💡 : 1: given? 🔍 🔹 two sides: 5 -12
🔹 there is/has: x (No )
🔹 : for x | 2: theorem 5 📐 theorem 5: all/every two sides > there is/has
🎯 there is theorem 5:
can be sides triangle?
💡 : 1: 🔍 | 5, 7, 10 |
|---|
| | there is/has | ? |
|---|
| 5 + 7 | 12 |
📐 theorem 6:
isosceles triangle, bisects angle , median altitude _____.
💡 : 1: theorem 🔍 theorem 6 ✨ isosceles triangle,
3 coincide:
1️⃣ bisects angle
2️⃣ median
3️⃣ altitude |
<
🎯 there is theorem 6:
triangle ABC isosceles (AB=AC), -A BC.
bisects angle A. ?
💡 : 1: given? 🔍 🔹 triangle ABC isosceles (AB = AC)
🔹 -A BC
🔹 bisects ∠A
🔹 : ? |
2: theorem 📐 th
🎯 there is theorem 6:
triangle ABC isosceles, altitude -A BC is at D.
BC = 16 cm, BD?
💡 : 1: given? 🔍 🔹 triangle ABC isosceles
🔹 altitude -A BC
🔹 altitude BC at D
🔹 BC = 16 cm
🔹 : BD = ? |
2: theorem 6 📐
📐 theorem 7:
triangle bisects angle is altitude, triangle is _____.
💡 : 1: theorem 🔍 theorem 7 ✨ triangle
bisects angle = altitude
triangle is/it is
is
📐 theorem 8:
triangle bisects angle is _____, triangle is isosceles.
💡 : 1: theorem 🔍 theorem 8 ✨ triangle
bisects angle = median
triangle is/it is
isos
📐 theorem 9:
triangle altitude is _____, triangle is isosceles.
💡 : 1: theorem 🔍 theorem 9 ✨ triangle
altitude = median
triangle is/it is
isosceles
🎯 there is theorem 7-9:
triangle ABC, -A BC at D.
given: ∠BAD = ∠CAD -BD = DC.
?
💡 : 1: given? 🔍 🔹 triangle ABC
🔹 AD -A BC
🔹 ∠BAD = ∠CAD → AD bisects ∠A
🔹 BD = DC → D is/it is BC
🔹 : ? |
2: 💭 AD is/it
📐 theorem 10:
triangle ( equal sides), opposite the side greater angle _____ .
💡 : 1: theorem 🔍 theorem 10 ✨ triangle ( equal sides), opposite the side greater/larger
🎯 there is theorem 10:
triangle ABC, sides: AB=5, AC=7, BC=9.
angle is greater ?
💡 : 1: given? 🔍 🔹 triangle ABC
🔹 AB = 5
🔹 AC = 7
🔹 BC = 9
🔹 : angle because greater/larger? |
2: angle opposite 💭 | angle | the side oppos
📐 theorem 11:
triangle ( equal angles), opposite angle greater _____ greater .
💡 : 1: theorem 🔍 theorem 11 ✨ triangle ( equal angles), opposite angle greater/larger
🎯 there is theorem 11:
triangle ABC, angles: ∠A=50°, ∠B=60°, ∠C=70°.
is ?
💡 : 1: given? 🔍 🔹 triangle ABC
🔹 ∠A = 50°
🔹 ∠B = 60°
🔹 ∠C = 70°
🔹 : because ? |
2: opposite angle 💭 | angle | |
📐 theorem 12:
angles triangle is _____.
💡 : 1: theorem 🔍 theorem 12 ✨ angles triangle
180°
! |
2: 180°? 💭
🎯 there is theorem 12:
triangle, two angles are 45° -75°.
angle there is?
💡 : 1: given? 🔍 🔹 angle 1 = 45°
🔹 angle 2 = 75°
🔹 angle 3 = ? |
2: theorem 📐 theorem
🎯 there is theorem 12:
triangle, angles are x, 2x, -3x.
x?
💡 : 1: given? 🔍 🔹 angle 1 = x
🔹 angle 2 = 2x
🔹 angle 3 = 3x
🔹 : x = ? |
2: theorem 📐 angl
📐 theorem 13:
exterior angle triangle equal _____ angles .
💡 : 1: exterior angle? 🔍 exterior angle angle
because triangle
is/it is triangle |
2: 📊
🎯 there is theorem 13:
triangle ABC, ∠A=40° -∠B=70°.
angle at C?
💡 : 1: given? 🔍 🔹 ∠A = 40°
🔹 ∠B = 70°
🔹 : angle at C |
2: theorem 📐 theorem 13:
exterior angle = two angles
|
🎯 there is theorem 13:
triangle, two angles are x -2x.
angle there is is 120°.
x?
💡 : 1: given? 🔍 🔹 angle 1 = x
🔹 angle 2 = 2x
🔹 angle there is/has = 120°
🔹 : x = ? |
2: theorem 📐
❓ :
exterior angle triangle greater
every one angles ?
💡 : 1: theorem 🔍 theorem 13:
exterior angle = ∠A + ∠B
(two angles ) |
2: 💭
🎯 theorem 12 -13:
triangle, angle one is 50°.
angle is ___?
💡 : 1: given? 🔍 2: are supplementary angles? 💭 supplementary angles = angles straight line
🎯 - theorem 1 -2:
two because. one angles is 55°.
angles 55° there is every?
💡 : 1: theorem 2 🔍 theorem 2:
vertical angles equal
there is/has angle 55°
angle also 55°
": 2 angles 55° |
2: angles ? 💭
🎯 - theorem 3 -4:
triangle, two sides equal two equal angles.
triangle ?
💡 : 1: 🔍 given:
🔹 two sides equal
🔹 two angles equal |
2: theorem 📐 theorem 3: opposite equal angles → sides equ
🎯 - theorem 5 -10:
triangle sides 4, 5, 8,
angle is greater ?
💡 : 1: - triangle? 🔍 theorem 5: two sides > there is/has
4 + 5 = 9 > 8 ✓
4 + 8 = 12 > 5 ✓
5 + 8 = 13 > 4 ✓
triangle ! |
2: theorem 10 📐
🎯 - theorem 6-9:
triangle, bisects angle is also altitude.
?
💡 : 1: 🔍 given:
bisects angle = altitude
theorem 7! |
2: theorem 7 📐
🎯 - theorem 12 -13:
triangle, two angles are 60° -80°.
angle there is?
💡 : 1: theorem 13 📐 theorem 13:
exterior angle = two angles
= 60° + 80°
= 140° |
: 140°
📚 every:
theorem triangles angles?
💡 13 theorem: | theorem |
|---|
| 1 | supplementary angles for 180° | | 2 | vertical angles equal | | 3 | op
🏆 :
isosceles triangle, angle the base is 40°.
angle ?
💡 : 1: theorem 4 🔍 isosceles triangle:
two base angles equal
one = 40°
two also = 40° |
2: theorem 13 📐 exterior angle
= two base angles
= 40
🏆 :
can be triangle angles: 120°, 130°, 140°? |
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