Sovi.AI - AI Math Tutor

Scan to solve math questions
ENFRDEESJAZH-CNZH-TW

QUESTION IMAGE

congruent? ○ yes ○ no similar? ○ yes ○ no

Question

congruent? ○ yes ○ no
similar? ○ yes ○ no

Explanation:

Step1: Analyze Congruent

Congruent figures have same shape and size. The two figures: one is an ellipse (stretched circle), the other is a circle. Their shapes differ (ellipse vs circle), so not congruent. So "Congruent? No".

Step2: Analyze Similar

Similar figures have same shape (proportional, same general form). Wait, no—wait, the first figure is an ellipse, second is a circle. Wait, maybe misperception: maybe the top is a circle stretched? Wait, no, the grid: let's check. Wait, maybe the top is a horizontal ellipse, bottom is a circle. But a circle is a special case of an ellipse (when major and minor axes equal). Wait, no—wait, maybe the top is a circle stretched horizontally, but the bottom is a circle. Wait, no, the bottom is a circle (symmetric in both axes), top is an ellipse (longer horizontally). Wait, but similar figures: for circles, all circles are similar. But if top is an ellipse (not a circle), then shape is different. Wait, maybe the top is a circle? Wait, the drawing: top is an oval (ellipse), bottom is a circle. So shape: ellipse vs circle—different. Wait, no, maybe the top is a circle stretched? Wait, no, in grid, let's count units. Suppose bottom circle has diameter 2 units (from grid), top ellipse: length (horizontal) 6 units, height (vertical) 2 units. So ellipse has major axis 6, minor 2; circle has diameter 2 (so radius 1, diameter 2, so both axes 2). So for similarity: two figures are similar if one can be obtained by scaling, rotating, translating the other. An ellipse and a circle: a circle is an ellipse with equal axes. But here, the top is an ellipse with unequal axes, bottom is circle (equal axes). Can we scale a circle to get that ellipse? Scaling a circle (which is uniform in x and y) would keep it a circle. To get an ellipse, we need non-uniform scaling (different in x and y). But similar figures require uniform scaling (same scale factor in x and y). Wait, no—similarity transformations include uniform scaling, rotation, translation, reflection. So if we scale a circle by factor 3 in x and 1 in y, we get an ellipse, but that's non-uniform scaling, which is not a similarity transformation (similarity transformations use uniform scaling). Therefore, the two figures (ellipse and circle) are not similar? Wait, no, maybe the top is a circle. Wait, maybe the drawing is a circle stretched horizontally, but the problem is maybe a misdraw. Wait, no—let's re-express: congruent means same shape and size. The two: one is larger (and stretched) than the other. So congruent? No. Similar: for circles, all circles are similar. But if top is a circle (maybe the drawing is a circle with horizontal stretch, but actually, in the grid, maybe the top is a circle with diameter 4, bottom with diameter 2? Wait, no, the bottom circle: let's say from grid, it's 2 units wide (diameter 2), top ellipse: 6 units wide, 2 units tall. So if we consider the top as an ellipse (not a circle), then shape is different. But if we consider the top as a circle (maybe the drawing is a circle, just drawn as an ellipse due to perspective), then: congruent? No (different sizes). Similar? Yes (all circles are similar, as scaling a circle gives another circle). Wait, maybe the top is a circle. Let's assume: bottom circle, top circle (maybe drawn as ellipse). Then:

Congruent? No (different sizes).

Similar? Yes (all circles are similar, since similarity for circles is just same shape, and circles have same shape regardless of size—scaling a circle preserves its shape).

Wait, the key: congruent requires same size and shape. Similar requires…

Answer:

Congruent? $\boldsymbol{\text{No}}$
Similar? $\boldsymbol{\text{Yes}}$